Dynamic analysis of the combustion cycle

During the combustion process of I.C. engine the fuel heat energy is converted to mechanical work. The working cycle of the I.C.engine is evaluated in terms of indicated power .  Empirical values of gas pressure force versus the crank angle are tabulated as shown below  to calculate the torque generated during the working cycle in conventional engine and oscillator engine.

Crank angle gas pressure Crank angle gas pressure force MPa force 0 0.018 370 5.402 30 -0.015 390 3.420 60 -0.015 420 1.350 90 -0.015 450 0.720 120 -0.015 480 0.450 150 -0.015 510 0.280 180 -0.015 540 0.150 210 -0.015 570 0.025 240 -0.015 600 0.018 270 0.020 630 0.018 300 0.150 660 0.018 330 0.720 690 0.018 360 1.923 720 0.018

Conventional piston/cylinder arrangement

In Cylinder/piston with crank gear arrangement the gas pressure force on piston is converted into rotary motion and torque of crank shaft. The actual driving force is the tangential component of the force acting on crank pin, which is equivalent to  T = P. sin(A+B)/ cosB . wherein the gas pressure forces exerted on the piston are brought on to crank pin are replaced with radial and tangential components of force. ( B is the crank angle counted off from the piston axis and A is the angle through which the connecting rod diverges from cylinder axis.)

Acting upon the crank pin, force directed from crank rod produces two components of forces.  Let the force directed along the crank radius be K.

       Then K=P cos{A+B}/ cosB  ( This massive component of force is spent as heat losses and frictional losses)

and let the force tangent to the crank radius circumference be T. Then    T = P sin(A+B)/ cosB ( This is the only component of force available to drive the crank gear)

The numerical values of the trigonometrically functions included for lambda = 0.27, if connecting rod length/ crank radius= lambda = 0.27

In this analysis we are deriving the torque generated to drive out put power and total value of work done per cycle event. Torsional moment(torque) of one cylinder (MN m) is determined by the value of  M= TxR ( Where R is the crank radius)

So, at any instance, Work done will be equal to:

                          torque x circumferencial distance traveled by the crank gear

To compare the total productive power imparted on drive shaft, we correlate  conventional engine and oscillator engine having similar swept volume of 1791822.37 cubic mm . ( This value is taken in to account as the equivalent volume of the selected oscillator engine)

For piston/ cylinder engine assume the Bore = Stroke.   Then the piston stroke (2R)

where Volume : 1791822.37 =R^3 x(22/7) x 2   so that R=65.814mm 

Now if we analyze the characteristics of conventional engine having crank radius of 65.81mm , we be able to compare with the characteristics of  oscillator engine.

The curve of Torque verses  the crank angle is plotted to compare the Total tortional moment generated during a combustion cycle.

Combustion chart for conventional engine

This graph shows the variation of value sin(A+B)/cosB with respect to gas pressure Vs crank angle. It clearly shows that involving this factor can decrease the efficiency by great amount. An example showing how the work done is calculated in the above chart Crank angle Gas pressure sin(A+B)/cosB Piston surface area F=PxA distance traveled by crank pin Average work done in 30degree 370 5.402 0.222 13,613.23102 16,325.58562 34.474 281,404.11927 390 3.420 0.625 13,613.23102 29,098.28130 34.474 782,971.19398 Take the example of about data: during the crank angle turning from 370 degrees to 390 degree gas pressure is assumed as 5.4002 MPa; and the Total force acted upon the connecting rod small end = Gas pressure x piston area There fore the tangential component of this force acting on crank pin to drive the shaft is  5.402 x.222 x  sin(A+B)/cosB = 5.402 x 13613.23 x 0.222 = 16325.58 MPa mm2 Within a 30 degrees angle Crank pin will travel a distance = 34.4743 Work done F s = 16325.58 x 34.474  within the specified turn of 30 degrees.

Oscillator engine arrangement

Equivalent oscillator engine having mobile flap surface area = 8450 mm2; distance from center to the point of action of resultant force = 67.4723;   distance traveled by this point within 30 degrees = 35.337mm. Tabulated data for the work done during a complete working cycle, due to gas pressure exerted on the flap surface is given below:

Graphical representation for Work done during a working cycle for both engine arrangements are plotted as shown below:

4353

Torque curves

The graph shows the torque generated during a working cycle in conventional engine and oscillator engine. Accordingly 1.55 times higher torque is generated in oscillator engine , for equal quantities of fuel burnt in both models.

                 Accordingly Work done in Oscillator engine during a working cycle   = 4353553.737

                 Work done in Conventional engine during a working cycle                  =    2803627.37

So that, 1.55 times higher torque will be generated in Oscillator engine arrangement, for same fuel consumption.

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