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Question 12.41: A single cylinder engine runs at 240 rpm and has a stroke of...

A single cylinder engine runs at 240 rpm and has a stroke of 200 mm. The reciprocating parts have a mass of 120 kg and the revolving parts are equivalent to a mass of 80 kg at a radius of 100 mm. A mass is placed opposite to the crank at a radius of 150 mm to balance the whole of the revolving mass and 2/3rd of the reciprocating mass. Determine the magnitude of the balancing mass and the resultant residual unbalance force when the crank has turned 30° from the inner dead centre. Neglect the obliquity of the connecting rod.

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N=240 rpm , L=200 mm , M=80 kg , R=120 kg , b=150 mm , c=2 / 3, \theta=30^{\circ} .

B b=(M+c R) r .

0.15 B=(80+2 \times 120 / 3) \times 0.1 .

B=106.67 kg .

\omega=2 \times 240 / 60=25.13 rad / s .

\text { Residual unbalanced force }= R \omega^{2} r \left[(1- c )^{2} \cos ^{2} \theta+ c ^{2} \sin ^{2} \theta\right]^{0.5} .

=120 \times(25.13)^{2} \times 0.1\left[(1-2 / 3)^{2} \times \cos ^{2} 30^{\circ}+4 \times \sin ^{2} 30^{\circ} / 9\right]^{0.5}.

= 3341.7 N.

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