A riveting machine is driven by a constant torgue 3kW motor. The moving parts including the flywheel are equivalent to 150 kg at 0.6 m radius. One riveting operation takes 1 second and absorbs 10000 N-in of energy. The speed of the flywheel is 300 rpm before riverting. Find the speed immediately after riveting. How many rivets can be closed per minute? -

Given:

P= 3kW; m = 150kg; r= 0.6m; El= 10000J; N1 = 300 rpm

Solution:

It is said that riveting can only be done when speed of the flywheel is 300rpm. When the riveting is done, the speed of the flywheel decreases, hence some time should be given to the flywheel to reach the 300rpm again. Hence, total time for one rivet = time for one rivet + time to wait before other rivet.

To find:

Total no. of rivets per minute

Total time for one rivet

Time to wait

Angular acceleration

Speed after riveting

Calculations:

$W = 2π300/60 = 31.4 rad/s \\ I = mr2/2 = 27 kg m^2$

Speed after riveting

Energy lost = change in KE

$E_l$ $= ½ \times I (w^2 – w_2^2) \\ = ½ x I \times ((2πN/60)^2 – w_2^2)$

$10000 = ½ x 27 \times (31.4^2 – w_2^2)$

$W_2 = 16.66 rad/s$

Angular acceleration

P $= T \times w_{avg} \\ = I \times α \times (w1 + w2)/2$

$3000 = 27 \times α \times (31.4 + 16.66)/2 \\ . α= 4.62 rad/s^2$

Time to wait

W2 = w1 + αt

31.4 = 16.66 + 4.62 x t

. t = 3.2 sec

Total time for one rivet

T = t + 1 = 3.2 + 1 = 4.2 sec