The method of direct and reverse cranks is applicable on reciprocating engines i.e V engines, radial engines, etc in which the piston performs reciprocating motion.
As shown in fig.1 (radial engine) and fig.2 (V-engine), the connecting rods are connected to a common crank and this crank revolve in one plane only. Hence there is no primary or secondary couple. Only primary and secondary force are required to be balanced.
(1) For determining the primary and secondary unbalanced forces.
(2) For balancing the primary and secondary unbalanced forces.
Fig-3
where, m = mass of reciprocating parts, kg
Fig-4
Fig-5
The primary direct crank OC makes an angle $\theta$ with line of stroke and is rotating uniformly at ‘$\omega$’ rad/s in clockwise direction whereas the primary reverse crank OCˊ makes an angle -$\theta$ with line of stroke and is rotating uniformly at ‘$\omega$’ rad/s in anticlockwise direction as shown in fig.5. Thus the primary reverse crank is mirror image of the primary direct crank.
The parameters of primary direct and reverse cranks:
I. Primary direct crank:
Angular position = $\theta$
Angular velocity = $\omega$ (clockwise)
Radius of crank = rII. Primary reverse crank:
Angular position = -$\theta$
Angular velocity = $\omega$ (anticlockwise)
Radius of crank = r
Let mass ‘m’ of reciprocating parts is divided into two equal parts (i.e. $m\over2$).
One of the parts is placed at direct crank pin ‘C’ and the other part is placed at reversed crank pin ‘C’ as shown in fig.5.
Centrifugal force acting on each mass placed at direct crank pin C and reverse crank pin
Hence, for determining the unbalanced primary force, the mass ‘m’ of the reciprocating parts can be replaced by two masses i.e. $m\over2$ each at point C and Cˊ respectively.
The vertical components of centrifugal force of masses (${m\over2}$) placed at point C and Cˊ are equal to ${m\over2}r\omega^2sin\theta$ , so these components are equal in magnitude and opposite in direction to each other. Hence, these components are balanced.
Fig-6
The parameters of secondary direct and reverse cranks:
I. Secondary direct crank:
Angular position = 2 $\theta$
Angular velocity = 2 $\omega$ rad/s (clockwise)
Radius of crank = ${r\over4n}$II. Secondary reverse crank:
Angular position = -2 $\theta$
Angular velocity = 2 $\omega$ rad/s (anticlockwise)
Radius of crank = $r\over{4n}$
Also read these important notes:
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