This document discusses balancing of reciprocating masses in locomotives. It begins by introducing the topic of today's lecture - balancing of reciprocating masses, the effect of partial balancing, and balancing primary forces in multi-cylinder engines. It then discusses partial balancing of locomotives, distinguishing between single and coupled locomotives. It explains the effect of partially balancing reciprocating parts in two-cylinder locomotives, noting it leads to unbalanced primary forces along and perpendicular to the stroke which cause variation in tractive force, a swaying couple, and hammer blow. Several examples are then given to calculate these values for given locomotive specifications running at various crank speeds. The document concludes by noting the topic of the next lecture will be numerical problems on balancing reciprocating

2. Previous lecture
Analysis for balancing of reciprocating masses

3. Today’s lecture
• Balancing of reciprocation masses
• Effect of Partial Balancing of
Reciprocating Parts
• Balancing of Primary Forces of Multi-
cylinder In-line Engines

5. Partial Balancing of
Locomotives
The locomotives, usually, have two cylinders with
cranks placed at right angles to each other in order
to have uniformity in turning moment diagram.

6. Partial Balancing of
Locomotives
Single or uncoupled locomotives
Coupled locomotives
A single or uncoupled locomotive is one, in which the effort is transmitted to one
pair of the wheels only ; whereas in coupled locomotives, the driving wheels are
connected to the leading and trailing wheel by an outside coupling rod.
https://www.youtube.com/watch?v=1QY2
USnwm08

7. Effect of Partial Balancing of Reciprocating Parts
of Two Cylinder Locomotives
Reciprocating parts are only partially balanced
Due to this partial balancing of the reciprocating parts, there is an unbalanced
primary force along the line of stroke and also an unbalanced primary force
perpendicular to the line of stroke.
Variation of Tractive Force
Swaying Couple
Hammer Blow

8. Variation of Tractive Force
The resultant unbalanced force due to the two cylinders, along the line of stroke, is
known as tractive force.

10. Swaying Couple
The unbalanced forces along the line of stroke for the two cylinders constitute a
couple about the centre line YY between the cylinders as shown in Fig

11. Hammer Blow
The maximum magnitude of the unbalanced force along the perpendicular to
the line of stroke is known as hammer blow.

12. An inside cylinder locomotive has its cylinder centre lines 0.7 m apart and has a stroke of
0.6 m. The rotating masses per cylinder are equivalent to 150 kg at the crank pin, and the
reciprocating masses per cylinder to 180 kg. The wheel centre lines are 1.5 m apart. The
cranks are at right angles.
The whole of the rotating and 2/3 of the reciprocating masses are to be balanced by masses
placed at a radius of 0.6 m. Find the magnitude and direction of the balancing masses.
Find the fluctuation in rail pressure under one wheel, variation of tractive effort and the
magnitude of swaying couple at a crank speed of 300 r.p.m.

15. Fluctuation in rail pressure

16. Variation of tractive effort
Swaying couple

17. The three cranks of a three cylinder locomotive are all on the same axle and are set at 120°. The
pitch of the cylinders is 1 metre and the stroke of each piston is 0.6 m. The reciprocating masses
are 300 kg for inside cylinder and 260 kg for each outside cylinder and the lanes of rotation of the
balance masses are 0.8 m from the inside crank.
If 40% of the reciprocating parts are to be balanced, find :
1. the magnitude and the position of the balancing masses required at a radius of 0.6 m ; and
2. the hammer blow per wheel when the axle makes 6 r.p.s.

21. Next lecture
• Numerical on balancing of
reciprocating masses

22. Contact details:
Rohit Kumar Singla
Email ID: rohit.kumar@thapar.edu