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

Qq

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

Qq

w

w

g

g

wallgaswallgasgr

radrad

F

TTTTh

A

Qq

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.