Balancing of Reciprocating Masses

1. Introduction

Reciprocating masses are parts of a machine that move back and forth (to and fro), such as:

• Piston
• Piston rod
• Crosshead

Balancing of reciprocating masses is the process of reducing or eliminating unbalanced inertia forces produced due to this motion.

2. Need for Balancing

• To reduce vibration
• To avoid excessive stresses on the frame
• To ensure smooth engine operation
• To increase machine life
• To reduce noise

3. Unbalanced Forces in Reciprocating Masses

Unlike rotating masses, reciprocating masses produce varying inertia forces.

Inertia Force

$$F = m \cdot a$$F=m⋅a

Where acceleration of piston:$$a = r \omega^2 \left(\cos \theta + \frac{r}{l} \cos 2\theta \right)$$

4. Primary and Secondary Forces

(a) Primary Force

$F_p = m r \omega^2 \cos \theta$

• Varies with $\cos \theta$cosθ
• Same frequency as crank rotation
• Can be partially balanced

(b) Secondary Force

$F_s = m r \omega^2 \frac{r}{l} \cos 2\theta$

• Varies with $\cos 2\theta$cos2θ
• Twice the crank frequency
• Difficult to balance completely

5. Methods of Balancing

(a) Partial Balancing

• Only a fraction of reciprocating mass is balanced
• Achieved by adding counterweights

(b) Complete Balancing

• Not possible practically for reciprocating masses
• Would introduce unbalanced forces in perpendicular direction

6. Balancing by Rotating Masses

• A portion of reciprocating mass is converted into equivalent rotating mass
• Counterweights are added on crank

Balancing Condition

$$m_b r_b = c \cdot m r$$mb​rb​=c⋅mr

Where:

• $c$c = fraction of reciprocating mass balanced

7. Hammer Blow and Swaying Couple

Hammer Blow

• Unbalanced vertical force on rails
• Caused by rotating balancing mass
• Important in locomotives

Swaying Couple

• Horizontal unbalanced force
• Causes side-to-side motion
• Affects stability

8. Balancing in Multi-Cylinder Engines

• Forces can be balanced by proper arrangement of cylinders
• Example:
  • 2-cylinder engines → partial balance
  • 4-cylinder engines → better balance
  • Opposed cylinder engines → excellent balance

9. Balancing of Locomotives

• Only partial balancing is done
• Excessive balancing → hammer blow
• Trade-off between:
  • Horizontal force
  • Vertical force

10. Advantages of Proper Balancing

• Smooth engine operation
• Reduced vibration
• Increased life of machine
• Less wear and tear
• Better efficiency

11. Limitations

• Complete balancing not possible
• Secondary forces remain
• Design compromise required

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