Two heavy rotating masses are connected by shafts of lengths l_1,l_2 and l_3 and the corresponding diameters are d1, d2 and d3. This system is reduced to a torsionally equivalent system having uniform diameter d = d1 of the shaft. The equivalent length of the shaft is

l_1 + l_2( d_1d_2 )^4 + l_3( d_1d_3 )^4

This question belongs to Mechanical Engineering Theory Of Machine

Theory of Machine

Two heavy rotating masses are connected by shafts of lengths $${l_1},\,{l_2}$$ and $${l_3}$$ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

A) $$\frac{{{l_1} + {l_2} + {l_3}}}{3}$$ B) $${l_1} + {l_2}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_2}}}} \right)^3} + {l_3}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_3}}}} \right)^3}$$ C) $${l_1} + {l_2}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_2}}}} \right)^4} + {l_3}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_3}}}} \right)^4}$$ D) $${l_1} + {l_2} + {l_3}$$

Answer & Solution

Correct Answer: Option C

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Two heavy rotating masses are connected by shafts of lengths l...

Two heavy rotating masses are connected by shafts of lengths $${l_1},\,{l_2}$$ and $${l_3}$$ and the corresponding diameters are d1, d2 and d3. This system is reduced to a torsionally equivalent system having uniform diameter d = d1 of the shaft. The equivalent length of the shaft is

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Two heavy rotating masses are connected by shafts of lengths $${l_1},\,{l_2}$$ and $${l_3}$$ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is