Estimate power produced by the engine:

A three cylinder two-stroke engine contains its cranks 120^o apart. The speed of the engine is equal to 600 rpm. The turning moment diagram for each of the cylinder may be represented through a triangle for one expansion stroke having a maximum value of one stroke having a maximum value of 600 Nm at angle 60^o from the top dead centre. The turning moment in other stroke is zero for all of the cylinders. Estimates :

 (a) The power produced by the engine,

 (b) The coefficient of fluctuation of speed along a flywheel having mass 10 kg and radius of gyration equivalent to 0.5 m,

 (c) The coefficient of fluctuation of energy, and

(d) The maximum angular acceleration of the flywheel.

Solution

The turning moment diagram of the engine is illustrated in given Figure. The resultant diagram is also illustrated which has shaded areas.

 (a)       Work done per cycle

Mean torque M _av = 900π/2π  = 450 Nm

∴          Power developed  

             = 450 × 2π 600

             = 9000 π

             = 28260 Watt

Or P =28260 kW

 (b)       Mass moment of inertia of the flywheel

'I' = m k²

= 10 × (0.5)²

= 2.5 kg m²

The fluctuation of energy is given by the shaded area above the mean line

                       Δ E = Ik_s w²

or,        78.54 = 2.5 k_s (62.8)²

Coefficient of fluctuation = 0.008.

 (c)       Coefficient of fluctuation of energy = Δ E/ E

                   Δ E = 78.5   and     E = 900π

Thus, coefficient of fluctuation of energy = 78.5 /900 π= 0.028

 (d)       Maximum excess torque = 600 - 450 = 150 Nm

Assume angular acceleration be 'α'.

∴          I α_max = 150

                    α_max= 150 /I = 150/2.5 = 60 r/s²