Partial Balancing of Locomotives

          The locomotives, usually, have two cylinders with cranks located at right angles (90°) to each other in order to have uniformly turning moment diagram and also the engine can be started easily after stopping in any position. Balance masses are placed on the wheels in both types. 

        In coupled locomotive, wheels are coupled by connecting their crank pins with coupling rods. As the coupling rod revolves with the crank pin, its proportionate mass can be considered as a revolving mass which can be completely balanced. 

Locomotive engines depending upon the location of cylinders they, are classified in two types they are:

           1. Inside cylinder engine and 2. Outside cylinder engine. 

          In the Inside cylinder locomotives, the two cylinders are placed in between the planes of two driving wheels as shown in Fig., Whereas in the Outside cylinder locomotives, the two cylinders are placed outside the driving wheels one on each side of the driving wheel, as shown in Fig., 

          They are further classified as Coupled and Uncoupled. If two or more pairs of wheels are coupled together to increase the adhesive force between the wheels and the track, it is called as coupled locomotive. otherwise, it is called as uncoupled locomotive.
          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 connecting rod.
          Thus, whereas in uncoupled locomotive, there are four planes for consideration, two of the cylinders and two of the driving wheels, In coupled locomotives there are six planes, two of cylinders, two of coupling rods and two of wheels. The planes which contain the coupling rod masses lie outside the planes that contain the balance (counter) masses. Also, in case of coupled locomotives, the mass required to balance the reciprocating parts is distributed among all the wheels which are coupled. Thus, results in a reduced Hammer Blow.

Effect of Partial Balancing of Reciprocating Parts of Two Cylinder Locomotives

          We have discussed in the previous article that the 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. 

          Locomotive engines operate at low speed and the ratio of length of connecting rod to radius of crank is generally large enough to neglect the effect of secondary force. 

The effect of an unbalanced primary force along the line of stroke is to produce:

1. Variation in tractive force along the line of stroke,  and 

2. Swaying couple

          The effect of an unbalanced primary force perpendicular to the line of stroke is to produce variation in pressure on the rails, which results in hammering action on the rails. The maximum magnitude of the unbalanced force along the perpendicular to the line of stroke is known as Hammer blow. 

Variation of Tractive Force

The tractive force is the reasultant unbalanced force due to the twi cylinders along the line of stroke. The unbalanced portion of the primary force which along the line of stroke causes the variation in the tractive force or effect. Let C is the friction of reciprocating masses that is balanced. Let the crank for the first cylinder be inclined at an angle θ with the line of stroke, as shown in Fig., Since the crank for the second cylinder is at right angle to the first crank, therefore the angle of inclination for the second crank will be (90° + θ).

Let        m  = Mass of the reciprocating parts per cylinder, and 

              C   = Fraction of the reciprocating parts to be balanced.

        We know that unbalanced force along the line of stroke for cylinder 1, 

         Similarly, unbalanced force along the line of stroke for cylinder 2,

As per defination the tractive force,

                         FT = Resultant unbalanced force along the line of stroke, 

The tractive force is maximum or minimum when (cos θ - sin θ)  is maximum or minimum.

For (cos θ - sin θ) to be maximum or minimum.

Maximum or minimum value of tractive force or the variation of tractive force is

Swaying couple

2. Swaying couple:

        The unbalanced portions of forces acting along the line of stroke are distance 'l' apart. These forces constitutes a couple about YY axis, which tends to make the leading wheels sway from side to side. This couple is known as swaying couple.

Note: In order to reduce the magnitude of the swaying couple, revolving balancing masses are introduced. But, as discussed in the previous article, the revolving balancing masses cause unbalanced forces to act at right angles to the line of stroke. These forces vary the downward pressure of the wheels on the rails and cause oscillation of the locomotive in a vertical plane about a horizontal axis. Since a swaying couple is more harmful than an oscillating couple, therefore a value of 'C' from 2/3 to 3/4, in two-cylinder locomotive with two pairs of coupled wheels, is usually used. But in large four cylinder locomotives with three or more pairs of coupled wheels, the value of 'C' is taken as 2/5.