For a single cylinder reciprocating engine speed is 500 rpm, stroke is 150 mm, mass of reciprocating parts is 21 kg; mass of revolving parts is 15 kg at crank radius. If two-thirds of reciprocating masses and all the revolving masses are balanced, the mass at a radius of 150 mm will be

Concept:

Balancing in the reciprocating engine

The unbalanced force due to reciprocating masses varies in magnitude but constant in direction while due to the revolving masses, the unbalanced force is constant in magnitude but varies in direction.

Unbalanced force,

\({F_U}\; = \;m.{ω ^2}.r\left( {cosθ + \frac{{cos2θ }}{n}} \right)\; = \;m.{ω ^2}.rcosθ + m.{ω ^2}.r × \frac{{cos2θ }}{n}\; = \;{F_P} + {F_S}\)

The expression (m. ω2.r cos θ) is known as primary unbalanced force and \(\left( {m.{ω ^2}.r × \frac{{cos2θ }}{n}} \right)\) is called secondary unbalanced force.

For primary balancing

m × r × ω² cosθ = B × b × ω2 cosθ 

∴ m × r = B × b

Where B is the balancing mass acting at the radius b

Calculation:

Given N = 500 rpm, b = 150 mm,

mass of reciprocating parts = m_c = 21 kg,

mass of revolving parts = m_r = 15 kg,

stroke = 150 mm ⇒ crank radius = r = 75 mm,

Total mass to be balanced is

\(m = \frac{2}{3}{m_c} + {m_r} = 14 + 15 = 29\;kg\)

Now

29 × 75 = B × 150 ⇒ B = 14.5 kg