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Paper Number 2006-01-0014
Analysis of an Extended Stroke, (Offset Crankshaft), EngineJohn J. Jibbencopyright 2005 SAE International
ABSTRACTThis is a fundamental analysis of an extended stroke, SI engine accomplished by comparing its performance to a typical engine with exactly the same piston data. The stroke extensions include the intake and power strokes, with longer crankshaft durations of 202 degrees, and the compression and exhaust strokes, with shorter crankshaft durations of 158 degrees. The primary focus of the analysis is to determine the impact on performance attributed solely to the mechanical differences of the two engines. This was accomplished by using an Air Standard Otto Cycle analysis which neutralized potential differences in combustion effects. The secondary focus is a qualitative discussion on potential improvements in combustion efficiency.
firing the ignition before TDC and beginning to open valves early, but mechanically the piston/crankshaft system has four identically sized crank-strokes, each being 180 degrees. If we could change the duration of the four crank-strokes to optimize performance what would we do? Given that the four-stroke Otto cycle consists of two complete revolutions of the crankshaft for a total of 720 degrees, and the piston moves through the same, identical pistonstroke for each crank-stroke, lets look at each stroke individually to see what makes sense intuitively. Starting with the intake stroke, we would want the crankstroke to be greater than 180 degrees, (again in all cases the piston-stroke remains constant). This allows more time for better breathing, and therefore, a more efficient process of charging the cylinder with the fuel/air mixture. Of course, we could still add multiple intake valves per cylinder and turbo-charge it to further improve breathing, but the act of extending the crank-stroke beyond 180 degrees could, in itself, potentially further improve breathing. The next stroke is compression, and here, reducing the crank-stroke to less than 180 degrees would potentially be an improvement. With the piston-stroke being constant, the compression would then occur more quickly and violently. This creates more turbulence for better fuel/air mixing and less time for compression blow-by. For the power stroke, we would want the crank-stroke to be greater that 180 degrees. This would allow more complete combustion because there would be more time to more thoroughly burn the fuel/air mixture. Thus, one would suspect more power would be produced with the same amount of fuel, resulting in an improvement in combustion efficiency. Finally, the exhaust stroke would probably want to have a crank-stroke that is more than 180 degrees as well to better purge the combustion gases. But to keep each revolution of the crankshaft at 360 degrees, it would have to be less than 180 degrees. This, however, is not a significant compromise, since we generally need to recycle some of the exhaust gases anyway to control NOx emissions.
INTRODUCTIONThe Otto cycle engine used in most automobiles today has undergone significant improvements since the oil embargo of the early 1970s. Improvements driven by environmental concerns, fuel costs, geopolitics, etc. have resulted in development of high energy ignition, multi-port fuel injection, turbo-charged, multi-valve breathing systems among other improvements that have resulted in significantly improved fuel efficiency and performance. However, the basic mechanical cycle defined by the Otto cycle has not changed. The pistons of a new, state of the art, four-stroke engine move up and down in the same manner as in a 1928 Ford Model A. This paper looks at a modification to the Otto cycle that may have the potential of providing improved fuel efficiency and performance. For the purposes of this paper, we need to define two terms. The Piston-stroke will refer to the distance the piston moves in the cylinder between top dead center (TDC) and bottom dead center (BDC). The Crank-stroke refers to the degrees of rotation of the crankshaft between TDC and BDC or BDC and TDC. The typical Otto cycle engine has four strokes, all of which have exactly the same crank-stroke duration, 180 degrees. In reality, we optimize the strokes somewhat by
This is all well and good, but how do you design an engine with two extended crank-strokes, (each greater than 180 degrees) and two with shorter crank-strokes, (less than 180 degrees)? One way to do this, without adding any moving parts, is to offset the crankshaft. Figures 1, and 2, show the piston/crankshaft relationship for both a typical or standard (STD) fourstroke engine and the piston/crankshaft relationship of an offset-crankshaft (OSC) engine, both with exactly the same piston-stroke, bore and clearance volume.
Figure 2, Piston Crankshaft Configuration with Offset Crankshaft
Figure 1, Piston Crankshaft Configuration for a Typical SI Engine
The crank circle in Figure 2, clearly shows that the clockwise angle of rotation of the crankshaft from TDC to BDC (intake and power strokes) is significantly larger than the angle from BDC to TDC (compression and exhaust strokes). Table 1, below, shows the crankshaft and cylinder data for these two engines. The OSC engine shown has power and intake strokes that are extended approximately 22 degrees; whereas, the piston-strokes of both engines are equal.
Notice that for the STD engine, the longitudinal center line of the cylinder passes through the cross-sectional center of the crankshafts main journal. For the OSC engine, the crankshaft is offset or translated to the left. Also, with both Figures 1, and 2, drawn to the same scale, the crank circle of the OSC engine is noticeable smaller than that of the STD engine. It can be shown mathematically that offsetting the crankshaft results in increasing the piston-stroke; thus, the radius of the crank circle of the OSC engine had to be reduced to maintain the same piston-stroke. It is obvious that with this large offset, the OSC connecting rod with its centerline on Line 1-2 will conflict with the cylinder. A bent rod approach centered on Line 1-3-2 will need to be used, as well as possibly a notched cylinder, to avoid the conflict.
Comp. Crank-stroke Power Crank-stroke Exhaust Crank-stroke Intake Crank-stroke Bore (b) Piston-stroke (d) Clearance Volume (VC) Displacement (Vd) Engine Speed (N) Adiabatic Pres. Increase Offset Distance (T) Offset Angle () Crank Length (S) Rod Length (L)
STD Engine 180 180 180 180 12.70 13.20 229.4 1901 2,000 3447 0.0 0.0 6.60 21.34
OSC Engine 158 degrees 202 degrees 158 degrees 202 degrees 12.70 cm 13.20 cm 229.4 cm3 1901 cm3 2000 rpm 3447 kPa 13.97 cm 30 degrees 5.08 cm 22.86 cm
Table 1, Engine Data for Comparable STD and OSC Engines
COMPARISON OF STD AND OSC ENGINESThe primary focus of the analytical analysis is to determine the effect on performance attributed solely to the mechanical differences of the two engines. Both engines operate on the Otto Cycle with exactly the same four strokes, except for changes in the duration of the crank-strokes resulting from offsetting the crankshaft of the OSC engine. The two engines we will compare will be the STD and OSC engines shown in Figures 1, and 2, and Table 1. Although single cylinder engines are being studied, the STD and OSC engine analysis also applies to multiple cylinder engines with in-line, V-type and other configurations. The STD engine is shown graphically in Figure 3, and the OSC engine in Figure 4. To compare the performance of these two engines, we need to compare various factors expressed as functions of crankshaft rotation such as piston motion, cylinder pressure, piston velocity, and torque. From these we can analyze and compare performance parameters. PISTON/CRANKSHAFT MOTION, STD ENGINE We will begin with developing equations that will describe the motion of the piston as a function of crankshaft rotation, D = f(), for the STD engine. For simplicity, we will look at only two of the four strokes, the compression stroke and the power stroke (one clockwise revolution of the crankshaft). The second revolution of the crankshaft, (exhaust and intake strokes), will be exactly the same.
For the compression stroke, where 0 180 degrees, and from Figure 3, basic geometry shows that
Eq 1. = arcsin sin (180 ) S L
Eq 2. D = d L S + L cos( ) S cos( )Substituting Eq 1, into Eq 2, we get D = f()
Eq 3. D = d L S + L cos arcsin sin ( ) S cos( ) S L For the power stroke, where 180 360 and from Figure 2, basic geometry as well shows that
Eq 1A. = arcsin sin ( ) S L
Eq 2A. D = d L S + L cos( ) S cos( )Substituting Eq 1A, into Eq 2A, we get D = f()
Eq 3A. S D = d L S + L cos arcsin sin ( ) S cos( ) L
Figure 3, STD Engine, Compression Stroke Diagram
Figure 4, OSC Engine, Compression Stroke Diagram
In summary, Eqs 3, and 3A, yield piston motion as a function of crankshaft rotation, or D = f() for 0 180 degrees and 180 360 degrees respectively for the STD engine. PISTON/CRANKSHAFT MOTION, OSC ENGINE Developing similar equations for piston motion for the OSC engine is a bit more complex, but a similar analysis from Figure 4, yields for the compression stroke, or 0 158 degrees.sin ( ) sin ( )
To calculate piston motion, D = f(), for the compression crank-stroke, we need to solve Eqs 3, 5, and 7 simultaneously as follows. For a specified value of , assume a value for D and calculate A from Eq 5. With this value of D, find the positive root of B in Eq 7, substitute it into Eq 3, and solve. If Eq 3, is not satisfied, repeat the process with a new value of D until Eq 3, is satisfied. This seems like a tedious process, but with the use of a personal computer, it is rather simple to zero in