Balancing of Secondary Forces of Multi-cylinder In-line Engines

          When the connecting rod is not long (i.e. when the obliquity of the connecting rod is considered), then the secondary distributing force due to the reciprocating mass arises.

We have discussed in previous articles, that the secondary force,

          As in case of primary forces, the secondary forces may be considered to be equivalent to the component, parallel to the line of stroke, of the centrifugal force produced by an equal mass placed at the imaginary crank of length r/4n and revolving at twice the speed of the actual crank (i.e. 2ω )  as shown in fig.,

          Thus in multi-cylinder in-line engines, each imaginary secondary crank with a mass attached to the crank pin is inclined to the line of stroke at twice the angle of the actual crank. The values of the secondary forces and couples may be obtained by considering the revolving mass. This is done in the similar way as discussed for primary forces. The following two conditions must be satisfied in order to give a complete secondary balance of an engine:

1. The algebraic sum of the secondary forces must be equal to zero. In other words, the secondary force polygon must close, and

2.   The algebraic sum of the couples about any point in the plane of the secondary forces must be equal to zero. In other words, the secondary couple polygon must close.

Note: The closing side of the polygon gives the maximum unbalanced secondary force and the closing side of the secondary couple polygon gives the maximum unbalanced secondary couple.

Balancing of Radial Engines (Direct and Reverse Cranks Method )

          The direct and reverse crank balancing method (also known as Contra-rotating mass balancing) aren't separate methods but rather one way of modelling the inertial effects of a reciprocating mass. The method of direct and reverse cranks is used in balancing of radial or V-Engines, in which the connecting rods are connected to a common crank. Since the plane of rotation of the various crank (in radial or V-Engines) is same, therefore there is no unbalanced primary or secondary couple. This is convenient for machines that have unaligned stroke centerlines (such as V-Engines and Rotary engines) since it eliminates the need to use "complicated Trigonometry".

          Consider a reciprocating engine mechanism as shown in above Fig (a)., Let the crank OC (known as the direct crank) rotates uniformly at 'ω' radians per second in a clockwise direction. Let at any instant the crank makes an angle 'θ'  with the line of stroke OP. The indirect or reverse crank OC' is the image of the direct crank OC, when seen through the mirror placed at the line of stroke. A little consideration will show that when the direct crank revolves in a clockwise direction, the reverse crank will revolve in the anticlockwise direction. We shall now discuss the primary and secondary forces due to the mass (m) of the reciprocating parts at P.

Considering Primary Forces: 
          We have already discussed that primary force is m.ω ².r cosθ . This force is equal to the component of the centrifugal force along the line of stroke, produced by a mass (m) placed at the crank pin C. Now let us support that the mass (m) of the reciprocating parts is divided into two parts, each equal to m/2 . 

          It is assumed that m/2 is fixed at the Direct Crank (termed as primary direct crank) pin C and m/2 at the Reverse crank (termed as primary reverse crank) pin C' , as shown in Fig (b).,

Hence, for primary effects of the mass m of the reciprocating parts at P may be replaced by two masses at C each of magnitude m/2.

Note:   The component of the centrifugal forces of the direct and reverse cranks, in a direction perpendicular to the stroke, are each equal to (m/2).ω ².r sinθ, but opposite in direction. are balanced.

Considering Secondary Forces:
          We know that the secondary force

         In the similar way as discussed above, it will be seen that for the secondary effects, the mass (m) of the reciprocating parts may be replaced by two masses (each m/2 placed at D and D' such that OD=OD'= r/4n. The crank OD is the secondary direct crank and rotates at 2 rad/s in the clockwise direction, while the crank OD' is the secondary reverse crank and rotates at 2 rad/s in the anticlockwise direction as shown in Fig (c).