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Question 12.29: The cranks and connecting rods of a four-cylinder in-line en...

The cranks and connecting rods of a four-cylinder in-line engine running at 2000 rpm are 50 mm and 200 mm each respectively. The cylinders are spaced 0.2 m apart. If the cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at intervals of 90° in an end view in the order 1–4–2–3, reciprocating mass for each cylinder is 2 kg. Determine (a) unbalanced primary and secondary forces, and (b) unbalanced primary and secondary couples with reference to central plane of engine.

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\text { Given: } l=200 mm , r=50 mm , n=\frac{200}{50}=4, N=2000 rpm , M=2 kg .

\omega=\frac{2 \pi N}{60}=\frac{2 \pi \times 2000}{60}=209.44 rad / s .

The position of cylinder planes is shown in Fig.12.48(a), with the central as the reference plane.

Table 12.29
Mrl (kg m²)
(6)		 Distance from
RP, l (m)
(5)		 Mr (kg m)
(4)		 Radius, r
(m)
(3)		 Mass, M
(kg)
(2)		 Plane
(1)
– 0.03 – 0.3 0.1 0.05 2 1
– 0.01 – 0.1 0.1 0.05 2 2
+ 0.01 + 0.1 0.1 0.05 2 3
+ 0.03 + 0.3 0.1 0.05 2 4

Primary force polygon: The primary crank position is shown in Fig.12.48(b). The primary force polygon has been drawn in Fig.12.48(c) with the data from column (4). There is no unbalanced primary force as the polygon in closed.

Primary couple polygon: The primary couple polygon is drawn in Fig. 4.31 (d) with the data in column

\text { (6). The unbalanced primary couple (UPC) }=d^{\prime} o^{\prime}=2.7 cm =0.027 .

\text { Unbalanced primary couple }=0.27 \times(209.44)^{2}=1184.36 N m .

Secondary force polygon: The secondary crank positions is shown in Fig. 4.31(e) by taking crank 3 as the reference crank. The secondary force polygon has been drawn in Fig. 4.31(f) with the data from column (4). There is no unbalanced secondary force as the polygon is closed.

Secondary couple polygon: The secondary couple polygon has been drawn in Fig. 4.31(g). The secondary unbalanced couple (USC) is proportional to,

USC =0.03+0.01+0.01+0.03=0.08 kg . m ^{2} .

or  USC =\frac{0.08 \times \omega^{2}}{n}=\frac{0.08 \times(209.44)^{2}}{4}=877.2 Nm .

12.48a
12.48aa
4.31

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