This document discusses partial balancing of reciprocating masses in engines. It provides an example of a single cylinder engine where two-thirds of the reciprocating mass and all of the revolving mass are balanced. It calculates the required balance mass and residual unbalanced force at 60 degrees from top dead center. It also gives an example of a four cylinder engine where the primary forces, secondary forces, and primary couples are balanced, and asks to determine the crank angle positions and mass of the reciprocating parts of the inner cylinders.

1. Balancing of Reciprocating Masses

9. Partial Balancing of Unbalanced Primary
Force in a Reciprocating Engine

10. know that centrifugal force due to mass B,
horizontal component of this force acting in opposite direction of primary
force
The primary force is balanced

11. compromise let a fraction ‘c’ of the reciprocating masses is balanced
Unbalanced force along the line of stroke

12. and unbalanced force along the perpendicular to the line of stroke
Resultant unbalanced force at any instant

13. If the balancing mass is required to balance the revolving masses as
well as reciprocating masses
Example 2.1. A single cylinder reciprocating engine has speed 240
r.p.m., stroke 300 mm, mass of reciprocating parts 50 kg, mass of
revolving parts at 150 mm radius 37 kg. If two-third of the reciprocating
parts and all the revolving parts are to be balanced, find: 1. the balance
mass required at a radius of 400 mm, and 2. the residual unbalanced
force when the crank has rotated 60° from top dead center.

15. 2. Residual unbalanced force

16. Hammer Blow

19. Example 2.2. A four cylinder engine has cranks arranged symmetrically
along the shaft as shown in Fig. 2.2. The distance between the outer cranks
A and D is 5.4 meters and that between the inner cranks B and C is 2.4
meters.
The mass of the reciprocating parts belonging to each of the outer
cylinders is 2 tones, and that belonging to each of the inner cylinders is m
tones. If the primary and secondary forces are to be balanced and also the
primary couples, determine the crank angle positions and the mass of the
reciprocating parts (m) corresponding to the inner cylinders.