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A single cylinder reciprocating engine has speed 240 r.p.m., stroke 300 mm, mass of reciprocating parts 50 kg, mass of revolving parts at 150 mm radius 37 kg. If two third of the reciprocating parts and all the revolving parts are to be balanced, find: 

1. The balance mass required at a radius of 400 ·mm, and 

2. The residual unbalanced force when the crank has rotated 60° from top dead centre.

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Given :N = 240 r.p.m. or  = 2 x 240/60 = 25.14 rad/s ; Stroke = 300 mm = 0.3 m; m = 50 kg; ml = 37 kg; r = 150 mm = 0.15 m ; c = 2/3

1. Balance mass required .

Let B : Balance mass required, and b : Radius of rotation of the balance mass: 400 mm : 0.4 m

We know that B.b: (m 1 + c.m) r

B x 0.4 : 10.55 or B : 26.38 kg

2. Residual unbalanced force 

Let Crank angle from top dead centre: 60° We know that residual unbalanced force.

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