A riverting machine is driven by a constant torque 3KW motor. The moving parts including the flywheel are equivalent to 150Kg mass and 0.6m radius. One riveting operation takes one second and absorbs 10000 N-m of energy. The speed of flywheel is 300 rpm before riverting. How many rivets can be closed per minute? -

Mumbai University > MECH > Sem 5 > Theory Of Machines 2

Marks: 10 M

Year: May 2015

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:

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

Speed after riveting

Energy lost = change in KE

$E_l$ $= ½ \times I (w^2 – w_2^2) \\ = ½ \times I \times ((2πN/60)^2 – w_2^2) \\ 10000 = ½ \times 27 \times (31.4^2 – w_2^2) \\ W_2 = 16.66 rad/s$

Angular acceleration

$P = T \times w_{avg} \\ = I \times α \times (w1 + w2)/2 \\ 3000 = 27 \times α \times (31.4 + 16.66)/2 \\ . α= 4.62 rad/s2$

Time to wait

$W2 = w1 + αt \\ 31.4 = 16.66 + 4.62 \times t \\ . t = 3.2 sec$

Total time for one rivet

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

Total no. of rivets per minute

$N= 60/T = 60/4.62 = 12.98 ≈ 13 rivets.$