Balancing of Reciprocating Masses

Chapter: 13

Balancing of Reciprocating Masses

Learning Objectives

While reading and after studying this chapter, you will be able to:

• Understand why complete balancing is not possible in reciprocating engines. 

• Differentiate between a primary unbalanced force and a secondary unbalanced force.

• Describe the effects of partial balancing of locomotive engines.

• Discuss the balancing of multi-cylinder in-line engines.

• Explain the direct and reverse crank method for determining unbalanced forces in radial engines.

• Describe a universal dynamic balancing machine indicating how balanced masses are found out.

SYLLABUS Balancing of reciprocating masses - Primary and secondary forces Partial balancing of locomotive engines - Balancing of multi-cylinder in-line engines - Balancing of radial engines - Balancing of V-engines - Balancing machines

INTRODUCTION

PRIMARY AND SECONDARY FORCES OF RECIPROCATING MASSÈS

It may be noted that in reciprocating engine mechanism, the inertia force F is the unbalanced force. Therefore the effect of inertia force should be eliminated for balancing. Therefore unbalanced force FU is given by

In equation (13.2), the first term i.e., m ω2 r cos θ is called as primary unbalanced force and the second term i.e., m ω2 r cos θ / n is called as secondary unbalanced force.

Note

From the expressions of primary and secondary unbalanced forces, the following points can be observed:

1. The primary unbalanced force is maximum when θ = 0° or 180°.

⸫ (FP)max = m ω2 r

2. The secondary unbalanced force is maximum when θ = 0°, 90°, 180° and 360°.

⸫ (FS)max = m ω2 r/n

3. From points (1) and (2), we see that the maximum value of the secondary unbalanced force is 1n times the maximum value of the primary unbalanced force.

4. As the value of n (ie., l/r), usually much greater than unity, the secondary unbalance force is small compared with the primary unbalanced force. Therefore the secondary unbalanced force can be safely neglected for low and moderate speed engines.

5. In case of high speed engines, the secondary forces are of appreciable magnitude and cannot be neglected.

6. Maximum value of the secondary unbalanced force occurs four times a revolution [see point (2)] as compared with twice per revolution for maximum primary unbalanced force [see point (1)]. In other words, we can say that the frequency of secondary unbalanced force is twice that of primary.

1. Revolving Mass cannot Completely Balance a Reciprocating Mass - Why? 

It is very important to note and understand that the unbalanced forces due to revolving masses (i.e., m ω2 r) remains constant in magnitude but varies in direction constantly with their motion. But the unbalanced forces due to reciprocating masses (i.e., m ω2 r cos θ and m ω2 r cos θ/n) remains constant in direction but varies in magnitude (because of variation in θ). Therefore, in general a revolving mass cannot completely balanced a reciprocating mass or vice versa.