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Kinematic Analysis for A Conventional I.C. Engine
P M V SubbaraoProfessor
Mechanical Engineering Department
Creation of Instantaneous Volume, Surface Area …..
Volume at any Crank Angle
Displacement Volume at Any Crank Angle
Relative location of piston center w.r.t . Crank Axis at any crank angle
Instantaneous Engine Cylinder Volume
Define Rod ratio
Identification of Events
Instantaneous compression ratio during compression
Instantaneous expansion ratio during expansion
Instantaneous Volume for A General Engine
Instantaneous Engine Cylinder Volume
Cylinder Surface Area at any Crank Angle
Macro Geometrical Parameters to be selected
• Engine Cylinder Volume: V
• Bore & Stroke of the cylinder: (B/l).
• Connecting Rod length Vs Crank radius (l/a).
• Engine Compression Ratio : (Vd/Vc+1).
Resulting Geometric Parameters of the Engine
• These parameters will have an influence on engine thermodynamic & mechanical performance.
For a general thermodynamic compression/expansion process:
ConstantnpV
nV
Cp
Kinetics of Engine Assembly & Generation of Primary Dynamic Forces
dt
d
d
dp
dt
dp
60
2 N
d
dp
dt
dp
60
21 NVd
dC
dt
dpn
60
2)1(
N
d
dV
V
nC
dt
dpn
22 sincos11
2
11 RRrVV cc
22 sincos11
2
1RR
d
drV
d
dVcc
60
2)1(
N
d
dV
V
nC
dt
dpn
Effect on Frictional Losses
• Engine friction is affected by the stroke-to-bore ratio because of two competing effects:
• Crankshaft bearing friction and power-cylinder friction.
• As the bore-to-stroke ratio increases, the bearing friction increases because the larger piston area transfers larger forces to the crankshaft bearings.
• However, the corresponding shorter stroke results in decreased power-cylinder friction originating at the ring/cylinder interface.
Instantaneous Heat Transfer (loss) form Cylinder
cg
coolantgas
hkx
h
TT
A
11
Gas to Surface Heat Transfer
• Heat transfer to walls is cyclic.
• Gas temperature Tg in the combustion chamber varies greatly over and engine cycle.
• Coolant temperature is fairly constant.
• Heat transfer from gas to walls occurs due to convection & radiation.
• Convection Heat transfer:
• Radiation heat transfer between cylinder gas and combustion chamber walls is
wallgasgcconv
conv TThA
w
w
g
g
wallgaswallgasgr
radrad
F
TTTTh
A
111
21
44
Cycle to Cycle Variation of Local Heat Flux:
Spatial Variation of Local Heat Flux:
Cooling of Piston
Computed Temperature of A Piston
Instantaneous Heat Transfer (loss) from Cylinder
Instantaneous surface area for heat transfer:
Piston Speed
Effect on Heat Transfer
• Simple geometric relationships show that an engine cylinder with shorter bore -to- stroke ratio will have a smaller surface area exposed to the combustion chamber gasses compared to a cylinder with longer bore-to- stroke ratio.
• The smaller area leads directly to reduced in-cylinder heat transfer, increased energy transfer to the crankshaft and, therefore, higher efficiency.
Optimum Cylinder Geometry
• Identification of the optimum engine geometry that provides the best opportunity to have a highly efficient internal combustion engine is the first step in designing an engine.
• In-cylinder simulations have shown that the heat transfer increases rapidly above a bore-to-stroke ratio of about 0.5.
• Engine systems simulations have shown that the pumping work increases rapidly above a bore=to-stroke ratio of about 0.45.
• Engine friction models have shown that the crankshaft bearing and power-cylinder friction values, for the most part, cancel each other out for our opposed-piston, two-stroke engine.
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