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of 3/15/2011 Variation torque of an engine crankshaft The torque on an engine crankshaft varies considerably throughout the working cycle, due to variations in the crank position, the pressure in the cylinder and the inertia of the moving parts. Crank Effort Diagrams Crank Effort Diagram Mean Torque If the crankshaft torque is plotted against the crank angle, a turning The net area of the diagram, shown shad ed, represents the wor k d one during the cycle and the ave rage h eight represents the m ean torque moment or crank effort diagram is obtained. exerted (line AE). Crank effort diagram for a single-cylinder four-stroke e ngine . Mean Torque Mean Torque If the resisting torque is uniform, this is equal to the mean engine torque if the mean speed is to remain constant. Engine torque > resisting torque (AB) Engine torque < resisting torque (BC) Engine speeds up; Engine slows down; At points of intersection (A, B C etc), Engine torque = resisting torque no acceleration or deceleration: speed is max. or min. at these points 1 3/15/2011 A turning moment diagram for a four stroke cycle internal combustion engine: In a four stroke cycle internal combustion engin e, there is one working stroke after the crank has turned through two revolutions, i.e. 720 (or 4 radians). Note: Since the pressure inside the engine cylinder is less than the atmospheric pressure during the suction stroke, therefore a negative loop is formed; During the compression stroke, the work is done on the gases, therefore a higher negative loop is obtained; Turning Moment Diagram for a Multi-cylinder Engine Note: During the expansion or working stroke, the fuel burns and the gases expand, therefore a large positive loop is obtained. In this stroke, the work is done by the gases. Turning moment diagram for a compound steam engine having three cylinders and the resultant turning moment diagram: During exhaust stroke, the work is done on the gases, therefore a negative loop is resultant formed. The turning moment diagram is the sum of the turning moment diagrams for the three cylinders. Fluctuation of speed and energy Fluctuation of speed and energy The horizontal line AG represents the mean torque line. Let a1, a3, a5 be the areas above the mean torque line and a2, a4 and a6 be the areas below the mean torque line. To keep the fluctuation of speed due to the variation of net torque within acceptable limits, a flywheel is fitted to the engine or machine shaft; its function is to act as a reservoir, absorbing energy as speed increases and releasing energy as speed falls. These areas represent some quantity of energy which is either added or subtracted from the energy of the moving parts of the engine. 2 3/15/2011 Fluctuation of speed and energy Fluctuation of speed and energy Fluctuation of speed and energy Fluctuation of speed and energy The excess e nergy available between the points of minimum and maximum speeds is called the fluctuation of energy and this represents the difference between the kinetic energies of the system at these points. If the maximum fluctuation of energy is U and 1 and 2 are the maximum and minimum speeds respectively between the cycle, then U 1 21 I 1 - I 2 2 2 2 where I is the moment of Inertia of the rotating parts. Coefficient of fluctuation of energy, CE The work done per cycle is represented by the area of the rectangle below the mean torque line and the ratio of fluctuation of energy to work done per cycle is called the coefficient of fluctuation of energy. U U 1 2 I ( 1 - 2 ) 2 2 1 I (1 - 2 ) (1 2 ) 2 Coefficient of fluctuation of energy The fluctuation of speeds, 1 - 2, is small in comparison with the mean speed and, assuming that the variations above and below the mean speed are equal, 1 2 2 U 1 I x 2 (1 2 ) 2 U I ( 1 2 ) 3 3/15/2011 Coefficient of fluctuation of speed The ratio (1 - 2)/, is called the coefficient of fluctuation of speed . Hence (1 2 ) U 2 I 4 ... View Full Document