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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)Analysis

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

Crank

angle

Gas pressure

force Mpa

 
sin(A+B)
cos B
Piston

area,mm2

Total force

Mpa.mm2

Distance traveled

by crank pin-mm

Work done

Mpa mm3

0 0.018 0.000 13,613.23102 0.00000 0 0.00000
30 -0.015 0.625 13,613.23102 -127.62404 34.474 -2,199.85559
60 -0.015 0.993 13,613.23102 -202.76908 34.474 -5,694.98615
90 -0.015 1.000 13,613.23102 -204.19847 34.474 -7,014.89951
120 -0.015 0.740 13,613.23102 -151.10686 34.474 -6,124.39796
150 -0.015 0.376 13,613.23102 -76.77862 34.474 -3,928.06214
180 -0.015 0.000 13,613.23102 0.00000 34.474 -1,323.43312
210 -0.015 0.376 13,613.23102 -76.77862 34.474 -1,323.43312
240 -0.015 0.740 13,613.23102 -151.10686 34.474 -3,928.06214
270 0.020 -1.000 13,613.23102 -272.26462 34.474 -7,297.65428
300 0.150 -0.993 13,613.23102 -2,027.69076 34.474 -39,644.33089
330 0.720 0.625 13,613.23102 6,125.95396 34.474 70,641.76273
360 1.923 0.000 13,613.23102 0.00000 34.474 105,593.06836
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
420 1.350 0.993 13,613.23102 18,249.21684 34.474 816,128.82536
450 0.720 1.000 13,613.23102 9,801.52633 34.474 483,510.66002
480 0.450 0.740 13,613.23102 4,533.20593 34.474 247,087.77996
510 0.280 0.376 13,613.23102 1,433.20096 34.474 102,842.95556
540 0.150 0.000 13,613.23102 0.00000 34.474 24,704.08497
570 0.025 -0.376 13,613.23102 -127.96437 34.474 -2,205.72187
600 0.018 -0.740 13,613.23102 -181.32824 34.474 -5,331.27670
630 0.018 -1.000 13,613.23102 -245.03816 34.474 -7,349.27756
660 0.018 -0.993 13,613.23102 -243.32289 34.474 -8,417.87941
690 0.018 -0.625 13,613.23102 -153.14885 34.474 -6,833.98338
720 0.018 0.000 13,613.23102 0.00000 34.474 -2,639.82671

Cumulative work done by piston in a working cycle( two revolutions). =2803627.37

GraphThis 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:

Combustion chart for oscillator engine
Flap   angle gas pressure force Flap surface area Force on flap lever arm Distance traveled Workdone Mpa.MM3
0 0.018 8,450. 152.100 67.4623 35.337 0.00000
30 -0.015 8,4500 -126.750 67.4623 35.337 447.89648
60 -0.015 8,4500 -126.750 67.4623 35.337 -4,478.96475
90 -0.015 8,450 -126.750 67.4623 35.337 -4,478.96475
120 -0.015 8,450 -126.750 67.4623 35.337 -4,478.96475
150 -0.015 8,450 -126.750 67.4623 35.337 -4,478.96475
180 -0.015 8,450 -126.750 67.4623 35.337 -4,478.96475
210 -0.015 8,450 -126.750 67.4623 35.337 -4,478.96475
240 -0.015 8,450 -126.750 67.4623 35.337 -4,478.96475
270 0.020 8,450 169.000 67.4623 35.337 746.49413
300 0.150 8,450 1,267.500 67.4623 35.337 25,380.80025
330 0.720 8,450 6,084.000 67.4623 35.337 129,889.97775
360 1.923 8,450 16,249.350 67.4623 35.337 394,596.79448
370 5.402 8,450 45,646.900 67.4623 35.337 1,093,613.89313
390 3.420 8,450 28,899.000 67.4623 35.337 1,317,114.23415
420 1.350 8,450 11,407.500 67.4623 35.337 712,155.39525
450 0.720 8,450 6,084.000 67.4623 35.337 309,048.56775
480 0.450 8,450 3,802.500 67.4623 35.337 174,679.62525
510 0.280 8,450 2,366.000 67.4623 35.337 108,988.14225
540 0.150 8,450 1,267.500 67.4623 35.337 64,198.49475
570 0.025 8,450 211.250 67.4623 35.337 26,127.29438
600 0.018 8,450 152.100 67.4623 35.337 6,419.84948
630 0.018 8,450 152.100 67.4623 35.337 5,374.75770
660 0.018 8,450 152.100 67.4623 35.337 5,374.75770
690 0.018 8,450 152.100 67.4623 35.337 5,374.75770
720 0.018 8,450 152.100 67.4623 35.337 5,374.75770
4353553.737

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.

We are pleased to receive your comments.

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Last Updated on 10/11/2007
By .LJayasuriya