Question

Consider a reciprocating engine with crank radius \( R \) and connecting rod of length \( L \). The secondary unbalance force for this case is equivalent to primary unbalance force due to a virtual crank of ________

• A. radius \( \frac{L^2}{4R} \) rotating at half the engine speed
• B. radius \( \frac{R}{4} \) rotating at half the engine speed
• C. radius \( \frac{R^2}{4L} \) rotating at twice the engine speed
• D. radius \( \frac{L}{2} \) rotating at twice the engine speed

Hint:

The secondary unbalance force in reciprocating engines is related to the crank radius and the connecting rod length, and it rotates at twice the engine speed.

Answer 1

The Correct Option is C

The secondary unbalance force in a reciprocating engine is equivalent to a primary unbalance force due to a virtual crank. The relationship for the radius of the virtual crank is derived from the geometry of the crank and the connecting rod. The virtual crank radius \( r \) is given by: \[ r = \frac{R^2}{4L} \] where:
- \( R \) is the crank radius,
- \( L \) is the connecting rod length.
The secondary unbalance force rotates at twice the engine speed because it corresponds to the frequency of the second harmonic of the crankshaft rotation. Thus, the correct answer is (C).