Question

The following data refer to two cylinder locomotive with cranks at ~Oo : Reciprocating mass per cylinder = 300 kg ; Crank radius = 0.3 m ; Driving wheel diameter = 1.8 m ; Distance between cylinder centre tines = 0.65 m ; Distance between the driving wheel central planes = 1.55 m. Determine 

1. the fraction of the reciprocating masses to be balanced, if the hammer blow is not to exceed 46 kN at 96.5 km. p.h. ;

2. the variation in tr active effort ; and

3. The maximum swaying couple.

Answer 1

Given: m = 300 kg ;r = 0.3 m ; D = 1.8 m or R = 0.9 m ; a = 0.65 m ; Hammer blow = 46 kN = 46 x 103 N ; v = 96.5 km/h = 26.8 m/s

 1. Fraction of the reciprocating masses to be balanced

Let c = Fraction of the reciprocating masses to be balanced, and B = Magnitude of balancing mass placed at each of the driving wheels at radius b. We know that the mass of the reciprocating parts to be balanced = c.m = 300 c kg

(b)  Position of cranks

The position of planes of the wheels and cylinders is shown in Fig.(a), and the position of cranks is shown in Fig(b). Assuming the plane of wheel A as the reference plane, the data may be tabulated as below:

Plane (1)	Mass (m) kg (2)	Radius (r) m (3)	Cent. force/ω2(m.r) kg-m (4)	Distance from plane A (l) m (5)	Couple/ω2(m.r.l.) kg-m2 (6
A (R.P.) B C D	B 300 c 300 c B	b 0.3 0.3 b	B.b 90 c 90 c B.b	0 0.45 1.1 1.55	0 40.5 c 99 c 1.55 B.b

Now the couple polygon, to some suitable scale, may be drawn with the data given in Table (column 6), as shown in Fig.. The closing side of the polygon (vector c₀) represents the balancing couple and is proportional to 1.55 B.b. From the couple polygon,

1.55 B.b = v((40.5c)2 + (99c) 2) = 107c

We know that angular speed, 00=vIR = 26.8/0.9 = 29.8 rad/s

 Hammer blow,

 46 x 103 = B.m2 .b = 69 c (29.8)2 = 61275 c

 c = 46 x 103/61275 = 0.751

2. Variation in tr active effort

 We know that variation in tr active effort 

= ± v2(l-c)m .. 002.r = ±v 2(1-0.751) 300 29.8f 

0.3 = 28 140 N = 28.14 kN

 Maximum swaying couple

 We know the maximum swaying couple