Balancing of Rotating Masses -- OBJECTIVE TYPE QUESTIONS

Balancing Of Rotating masses

Objective type questions

1. The balancing of Rotating and Reciprocating parts of the engine is necessary when it runs at

(a) Slow speed                                         (b) Medium speed 

(c) High speed                                         (d) No speed

2. Which of statements is true for static balancing of shaft,

(a) The net dynamic forces acting on the shaft is zero           
(b)  The net couple due to dynamic forces acting on the shaft is zero

(c) Both (a) and (b)                          (d) None of the above statements

3. For Dynamic balancing of shaft,

(a) The net dynamic forces acting on the shaft is zero           
(b)  The net couple due to dynamic forces acting on the shaft is zero

(c) Both (a) and (b)                          (d) None of the above statements

4. Which of the following statements is correct about the balancing of a mechanicalsystem?

(a) If it is under Static balance, then there will be dynamic balance too           
(b)  If it is under Dynamic balance, then there will be Static balance too

(c) Both Dynamic and Static balance have to be achieved separately
(d) None of the above mentioned statements

5. A distributing mass m₁ attached to a rotating shaft may be balanced by a single mass m₂ attached in the same plane of ratation as that of m₁ such that 

(a) m₁.r₂ = m₂.r₁           
(b)  m₁.r₁ = m₂.r₂

(c) m₁. m₂ = r₁.r₂

6. Which of the following statements are associated inorder to have a complete balancing of the several revolving masses in different planes 

(a) The resultant couple must be zero           
(b) The resultant force must be zero

(c) Both resultant force and couple must be zero
(d) None of the above

7. Which of the following statements are associated with complete dynamic balancing of rotating systems? 

(1) The resultant couple due to all inertia forces is zero           
(2) The support reactions due to forces are zero but not due to couples

(3) The system is automatically statically balanced
(4) Centre of masses of the system lies on the axis of rotation

(a) 1, 2 and 3 only           (b) 2, 3 and 4 only

(c) 1, 3 and 4 only           (d) 1, 2, 3 and 4 

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).

Balancing of V-engines

Consider a symmetrical two cylinder V-Engine as shown in Fig., The common crank OC is driven by two connecting rods PC and QC. The lines of stroke OP and OQ are inclined to the vertical OY, at an angle α as shown in Fig.,

Let                          m= Mass of reciprocating parts per cylinder,

                                l = Length of connecting rod, 

                                r = Radius of crank,

                                n= Ratio of length of connecting rod to crank radius = l/r

                                θ = Inclination of crank to the vertical at any instant,

                                ω  = Angular velocity of crank.

We know that inertia force due to reciprocating parts of the cylinder 1, along the line of stroke, 

and the inertia force due to reciprocating parts of the cylinder 2, along the line of stroke,

The balancing of V-Engines is only considered for primary and secondary forces as discussed below:

Considering primary forces:

Considering secondary forces: