Question

A shaper is driven by an electric motor which supplies the power at an uniform rate of 0.8 kW. The crank of the shaper runs at 20 rpm and the quick return ratio is 2. A flywheel of moment of inertia $150kg-m^2$ controls the speed fluctuation . Assuming that the power required only during the cutting stroke, the fluctuation of speed of the flywheel as a percentage of mean speed of 200 rpm is.

• A. 1.2 %
• B. 2.4 %
• C. 1.6 %
• D. 3.2 %

Answer 1

The correct option is A 1.2 %

$\text{Power},P=0.8kW,I=150kg-m^2$

$N_{mean}=200rpm$

${\omega }_{mean}=\frac{2\pi N_{mean}}{60}=\frac{2\pi \times 200}{60}=20.943rad/sec$

20 rev $\to$ 60 sec

$1rev\to \frac{60}{20}=3sec\left(cycletime\right)$

$QRR=2=\frac{\text{Time for cutting stroke}}{\text{time for return stoke}}$

Cutting stroke time = 2 sec,

Return stoke time = 1sec

Maximum fluctuation of energy =$\Delta E$

Power$\times$ cycle time

=0.8$\times$ 1 = 800 J

$\Delta E=I{\omega }_{mean}^2{C}_s$

$C_s=\frac{800}{150\times (20.943{)}^2}=0.012=1.2\%$