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 Reciprocating Masses -- Introduction

Introduction

          We have discussed in previous chapters, the various forces acting on the reciprocating parts of an engine. The result of all the forces performing on the body of the engine due to inertia forces only is known as unbalanced force or shaking force.  Thus if the resultant of all the forces due to inertia effects is zero, then there'll be no unbalanced force, however even then an unbalanced couple or shaking couple will be present. 

          Consider a horizantal reciprocating engine mechanism as shown in below Fig.,

Let   F_R  = Force required to accelerate the reciprocating parts,

         F_I   = Inertia force due to reciprocating parts,

         F_N  = Force on the sides of the cylinder walls or normal force acting on the cross-head guides, and

         F_B  = Force acting on the crankshaft bearing or main bearing.

          Since F_R and F_I are equal in magnitude however act in opposite direction, therefore they balance one another. The horizantal component of F_B (i.e F_BH) acting along the line of reciprocation is also equal and opposite to F_I. This force F_{BH =} F_U is an unbalanced force or shaking force and required to be properly balanced.

         The force on the sides of the cylinder walls (F_N) and the vertical component of  F_B(i.e F_BV) are equal and opposite and thus form a shaking couple of magnitude  F_N X x _or F_BV X x. 

          From the above statements we tend to see that the imapct (or) effect of the reciprocating parts is to produce a shaking force and a shaking couple. Since the shaking force and a shaking couple differ in magnitude and direction during the engine cycle, therefore they cause terribly objectionable vibrations.

          Thus the purpose (or  aim) of balancing the reciprocating masses is to eliminate the shaking force and a shaking couple. In most of the mechanisms, we can produce the shaking force and a shaking couple by adding appropriate balancing mass, But it is usually not practical to eliminate them completely. In otherwords, the reciprocating masses are only partially balanced. 

Note : The masses rotating witht he crankshaft are normally balanced and they do not transmit any unbalanced or shaking force on the body of the engine.

Primary and secondary Unbalanced Forces of Reciprocating masses

          Consider a reciprocating engine mechanism as shown in Below Fig., 

                    Let m = Mass of reciprocating parts,

                           l = Length of connecting rod PC, 

                           r = Radious of the crank OC, 

                          Θ = Angle of inclination of the crank with the line of stroke PO,

                          ω = Angular speed of the crank,

                      η = Ratio of length of the connecting rod to the crank radious = l/r

          We have already discussed in previous articles that the acceleration of the reciprocating parts is approximatey given by expression, 

          Inertia force due to reciprocating parts or force required to accelerate the reciprocating parts,

We have discussed in the previous article that the horizantal component of the force exerted on the crank shaft bearing (i.e F_BH ) is equal and opposite to inertia force (F1). This force is an unbalanced one and is denoted by F_U  .

Unbalanced force 

          The expression (m.ω^2 .r cos Θ) is known as Primary unbalnced force and (m.ω^2 .r [cos 2Θ]/n ) is called secondary unbalanced forces.

Partial Balancing of Unbalanced Primary Force in a reciprocating Engine

          The primary unbalanced force may be considered as the component of the centrifugal force produced by a rotating mass 'm' placed at the crank radius 'r' as shown in below Fig.,

          The primary force act from O to P along the line of stroke. Hence, the balancing of primary force is considered as equivalent to the balancing of mass 'm' rotating at the crank radius 'r'. This is balanced by having a mass B at radius b, placed diametrically opposite to the crank pin C. 

We know that centrifugal force due to mass B, 

                              = B. w^2. b.
and horizantal component of this force acting in opposite direction of primary force
                              = B. w^2. b cos θ.
The primary force is balnced if 
                    B. w^2. b cos θ = m w^2. r cos θ 
                                                 or
                     B.b = m. r
          A little consideration will show, that the primare force is completely balanced if B.b = m. r , but the centrifugal force produced due to the revolving mass B, has also a vertical  component perpendicular to the line of stroke having magnitude B. w^2. b sin θ. This force remains unbalnced. The maximum of this force occurs at value of θ = 90° or 270°. 
          From the above discussion we know that there are two unbalced force, one along the line of stroke where as the second unbalnced force acts along the perpendicular to the line of stroke. The maximum valve of force remains same  in both the cases.It is thus obvious, that the effect of the above method of balancing is to change the direction of the maximum unbalnced force from the line of stroke to the perpendicular of line of stroke. A compromise let a fraction 'c' of the reciprocationg masses is balnced such that