MEC 461 IC Engines
Chapter 2: Engine Components, operating parameters
and characteristics
Geometric Properties
VC
TC
y
Piston displacement: y = l + a - s
B
(
s = a cosθ + l 2 − a 2 sin 2 θ
L
BC
Wrist pin
Connecting rod
1/ 2
When the piston is at TC (s= l+a) the cylinder
volume equals the clearance volume Vc
The cylinder volume at any crank angle is:
l
s
)
V = Vc + Ac y = Vc +
πB 2
4
(l + a − s )
Maximum displacement, or swept, volume:
θ
a
Vd =
πB 2
4
L
Compression ratio:
For most engines B ~ L
(“square engine”)
rc =
VBC Vc + Vd
=
VTC
Vc
2
Geometric Properties
VC
TC
B
Average piston velocity:
U p = 2 LN
L
BC
l
s
 stroke  m  rev 




 rev  stroke  s 
Average piston speed for standard auto engine is
about 15 m/s. Ultimately limited by material
strength. Therefore engines with large strokes run
at lower speeds
“Over square engines” (B > L) with light pistons
have higher rev limits
(
s = a cosθ + l 2 − a 2 sin 2 θ
θ
a
)
1/ 2
Instantaneous piston velocity:
Up =

cosθ
= sin θ 1 +
Up 2

(l / a )2 − sin 2 θ


1/ 2

Up
π
(
ds
dt
)
3
Piston Velocity vs Crank Angle
R = l/a
R=3
TC
BC
4
Piston Acceleration
1/ 2
  a 2 2 
Piston displacement is: s = a cosθ + l 1 −   sin θ 

 l


For most modern engines (a/l)2 ~ 1/9
Using series expansion approximate (1-ε)1/2 ~ 1-(ε/2) and subst θ = ωt
So
Substituting
yields
differentiating
2
 a

s = a cos ωt +  l − sin 2 ωt 
 2l

sin 2 ωt = (1 − cos 2ωt ) / 2
2
 a

s = a cos ωt +  l − (1 − cos 2ωt ) 
 4l

d 2s
a

2
=
a
ω
cos
ω
t
+
cos
2
ω
t


l
dt 2


5
Torque and Power
Torque is measured off the output shaft using a dynamometer.
b
Force F
Stator
Rotor
N
Load cell
The torque exerted by the engine is T:
T = F ⋅b
units : Nm = J
The power W delivered by the engine turning at a speed N and
absorbed by the dynamometer is:
W = ω ⋅ T = (2π ⋅ N ) ⋅ T
 rad  rev 
units : 
( J ) = W (1 kW = 1.341 hp )

 rev  s 
Note: ω is the shaft angular velocity in units rad/s
6
Brake Power
Torque is a measure of an engine’s ability to do work and power is
the rate at which work is done
Note torque is independent of crank speed.
The term brake power, Wb , is used to specify that the power is
measured at the output shaft, this is the usable power delivered by
the engine to the load.
The brake power is less than the power generated by the gas in
the cylinders due to mechanical friction and parasitic loads (oil
pump, air conditioner compressor, supercharger, etc…).
The power produced in the cylinder is termed the indicated
power,Wi .
7
Indicated Work per Cycle
Given the cylinder pressure data over the operating cycle of the engine one
can calculate the work done by the gas on the piston. This data is
typically given as P vs V
The indicated work per cycle is given by Wi = ∫ PdV
Compression
W<0
Power
W>0
Exhaust
W<0
Intake
W>0
8
Indicated Work per Cycle
Given the cylinder pressure data over the operating cycle of the engine one
can calculate the work done by the gas on the piston. This data is
typically given as P vs V
The indicated work per cycle is given by Wi = ∫ PdV
WA > 0
A
C
WB < 0
Compression
W<0
Power
W>0
Exhaust
W<0
Intake
W>0
9
Work per Cycle
Gross indicated work per cycle – net work delivered to the piston over
the compression and expansion strokes only:
Wi,g = area A + area C (>0)
Pump work – net work delivered to the gas over the intake and exhaust
strokes:
Wp = area B + area C (<0)
Net indicated work per cycle – work delivered over all strokes:
Wi,n = Wi,g – Wp = (area A + area C) – (area B + area C)
= area A – area B
10
Indicated Power
Indicated power:
WN
Wi = i
nR
(kJ cycle)(rev s )
rev cycle
where N – crankshaft speed in rev/s
nR – number of crank revolutions per cycle
= 2 for 4-stroke
= 1 for 2-stroke
Power can be increased by increasing:
• the engine size, Vd
• compression ratio, rc
• engine speed, N
11
Indicated Work at WOT
The pressure at the intake port is just below atmospheric pressure
Po
Pintake
Pintake
The pump work (area B+C) is small compared to the gross indicated
work (area A+C)
Wi,n = Wi,g - Wp = area A - area B
12
Indicated Work at Part Throttle
The pressure at the intake port is significantly lower than atmospheric pressure
Pintake
The pump work (area B+C) can be significant compared to gross indicated
work (area A+C)
Wi,n = Wi,g - Wp = area A - area B
13
Indicated Work with Supercharging
Engines with superchargers or turbochargers have intake pressures
greater than the exhaust pressure, yielding a positive pump work
Compressor
Pintake
Wi,n = area A + area B
Supercharge increases the net indicated work but is a parasitic load
since it is driven by the crankshaft
14
Mechanical Efficiency
Some of the power generated in the cylinder is used to overcome engine
friction and to pump gas into and out of the engine.
The term friction power, W f , is used to describe collectively these power
losses, such that:
W f = Wi , g − Wb
Friction power can be measured by motoring the engine.
The mechanical efficiency is defined as:
W f
Wb Wi , g − W f
=
= 1−
ηm =


Wi , g
Wi , g
Wi , g
15
Mechanical Efficiency, cont’d
Mechanical efficiency depends on pumping losses (throttle position) and
frictional losses (engine design and engine speed).
Typical values for automobile engines at WOT are:
90% @2000 RPM and 75% @ max speed.
Throttling increases pumping power and thus the mechanical efficiency
decreases, at idle the mechanical efficiency approaches zero.
16
Power and Torque versus Engine Speed at WOT
W ∝ N ⋅ T and W ∝ N ⋅ Wcycle
Rated brake power
1 kW = 1.341 hp
so
T ∝ Wcycle
There is a maximum in the brake power
versus engine speed called the rated
brake power (RBP).
At higher speeds brake power decreases as
friction power becomes significant compared
to the indicated power Wb = Wi , g − W f
Max brake torque
There is a maximum in the torque versus
speed called maximum brake torque (MBT).
Brake torque drops off:
• at lower speeds due to heat losses
• at higher speeds it becomes more difficult to
ingest a full charge of air.
17
Indicated Mean Effective Pressure (IMEP)
imep is a fictitious constant pressure
that would produce the same work per
cycle if it acted on the piston during the
power stroke.
Wi Wi ⋅ nR
imep ⋅ Vd ⋅ N
imep =
=
→ Wi =
Vd Vd ⋅ N
nR
=
imep ⋅ Ap ⋅ U p
2 ⋅ nR
Brake mean effective pressure
(bmep) is defined as:
bmep =
Wb 2π ⋅ T ⋅ nR
=
Vd
Vd
→ T=
bmep ⋅ Vd
2π ⋅ nR
imep is a better parameter than torque
to compare engines for design and
output because it is independent of
engine size, Vd.
18
The maximum bmep of a good engine design is well established:
Four stroke engines:
SI engines: bmep= 850-1050 kPa*
CI engines: bmep= 700 -900 kPa
Turbocharged SI engines: bmep= 1250 -1700 kPa
Turbocharged CI engines: bmep= 1000 - 1200 kPa
Two stroke engines:
Standard CI engines comparable bmep to four stroke
Large slow CI engines: 1600 kPa
*Values are at maximum brake torque and WOT
Note, at the rated (maximum) brake power the bmep is 10 - 15% less
Can use the maximum bmep in design calculations to estimate engine
displacement required to provide a given torque or power at a specified
engine speed.
19
Maximum BMEP
bmep =
Wb 2π ⋅ T ⋅ nR
=
Vd
Vd
The maximum bmep is obtained at WOT at a particular engine speed
Closing the throttle decreases the bmep
For a given displacement, a higher maximum bmep means more torque
For a given torque, a higher maximum bmep means smaller engine
Higher maximum bmep means higher stresses and temperatures in the
engine hence shorter engine life, or bulkier engine.
For the same bmep 2-strokes have almost twice the power of 4-stroke
20
Road-Load Power
A part-load power level used for testing engines (fuel economy, emissions)
is the power required to drive a vehicle on a level road at a steady speed.
The road-load power, Pr , is the engine power needed to overcome
rolling resistance and the aerodynamic drag of the vehicle.
Pr = (C R M v g + 1 ρ a C D Av Sv2 ) ⋅ Sv
2
where CR = coefficient of rolling resistance (0.012 - 0.015)
Mv = mass of vehicle
g = gravitational acceleration
ρa = ambient air density
CD = drag coefficient (for cars: 0.3 - 0.5)
Av = frontal area of the vehicle
Sv = vehicle speed
*Modern midsize aerodynamic cars only need 5-6 kW (7-8 HP)
to cruise at 90 km/hr, hence the attraction of hybrid cars!
21
Drag Force Parameters
Auto manufacturers can improve the drag force by reducing:
Vehicle frontal area:
2005 Corvette is 0.57 m2
Most cars around 0.8 m2
2006 Hummer H3 is 1.56 m2
Drag coefficient CD:
2004 Toyota Prius – 0.26
2005 Porsche Boxster – 0.29
1983 Audi 100 – 0.3
2006 Dodge Challanger – 0.33
2003 Hummer – 0.57
Formula 1 car – 0.7 to 1.1 (DRS)
Drag Reduction System
22
Engine power requirements
α
F=Mvg
For a 1500 kg car moving at 50 km/hr up a 10o incline:
PC = ( M v g sin α ) ⋅ S v = 35 kW = 47 hp
F = Mva
For a 1500 kg car accelerating (constant) from 0-100 km/hr in 8 s:
Pa = M v ( S v / t ) ⋅ S v = 145 kW = 207 hp
Ferrari 430 Scuderia produces 508 hp at 8500 rpm (4.3L V8 engine).
It weighs 1270 kg and 0-100 km/hr in 3.6 s requires 272 kW (389 hp)
23
Automobile transmission
Engine operates between 600 – 7000 rpm whereas car wheels rotate at
0 -1800 rpm
Highest torque is obtained in the mid engine speed range while the
greatest torque is often required at the lowest wheel speed
Transmission produces high torque at low car speeds and also operates
at highway speeds with the engine operating in the same speed range
 transmission changes the gear ratio as the car speeds up
Automatic transmission – gears shift automatically based on input
data from the sensors on the engine and the transmission (e.g., engine
speed, vehicle speed, throttle position, brake pedal position)
Manual transmission – operator shifts gears
24
Gears
Gears change the speed of rotation and torque transmitted between shafts
Consider a simple gear set consisting of two gears:
ωo
ωi
Ri
Ro
GR =
Ro
Ri
Vc, Fc
Gear ratio (GR) is the number of turns of the input shaft required to give one
revolution of the output shaft
Vc = ωi Ri = ωo Ro
Fc = Ti / Ri = To / Ro
 Ri 
ωi
ωo =  ωi =
GR
 Ro 
 Ro 
To =  Ti = GR ⋅ Ti
 Ri 
25
Automobile Transmission
An automobile is more complicated because you need several gear
ratios so the car can accelerate smoothly (shift for power or fuel
economy?)
Automatic transmission uses two sets of planetary gears to give three
or four forward gear ratios and one reverse
Manual transmission typically has five forward gears and a reverse
Gear
GR
ωo/ωi
To/Ti
1
3:1
1/3
3
2
2.5:1
2/5
5/2
3
1.5:1
2/3
3/2
4
1:1
1
1
0.75:1
4/3
3/4
5 (OD)
26
500
1999 Neon DOHC
Engine
1st gear (GR=3.54)
2nd gear (GR=2.13)
3rd gear (GR=1.36)
4th gear (GR=1.03)
5th gear (GR=0.72)
450
400
Torque (Ft-lb)
350
ω2 nd =
GR2
ω1st
GR1
300
250
4210 rpm
3610 rpm
200
150
100
50
0
0
1000
2000
3000
4000
5000
6000
7000
8000
Engine speed (RPM)
27
Specific Fuel Consumption
For transportation vehicles fuel economy is generally given as mpg, or
L/100 km (in the future gm of CO2/km).
In engine testing the fuel consumption is measured in terms of the fuel
mass flow rate m f .
The specific fuel consumption, sfc, is a measure of how efficiently the
fuel supplied to the engine is used to produce power,
m f
bsfc =
Wb
m f
isfc =
Wi
units :
g
kW ⋅ hr
Clearly a low value for sfc is desirable since for a given power level
the lesser the fuel consumed the better it is.
28
Brake Specific Fuel Consumption vs Engine Size
Bsfc decreases with engine size due to reduced heat losses from gas to
cylinder wall.
Note cylinder surface to volume ratio increases with bore diameter.
heat loss
cylinder surface area πBL
1
=
= 2 ∝
energy released
cylinder volume
πB L B
29
Brake Specific Fuel Consumption vs Engine Speed
There is a minimum in the bsfc versus engine speed curve
bsfc =
m f
Wb
At high speeds the bsfc increases due to increased friction i.e. smaller Wb
At lower speeds the bsfc increases due to increased time for heat
losses from the gas to the cylinder and piston wall, and thus a smaller Wi
Bsfc decreases with compression ratio due to higher thermal efficiency
30
Performance Maps
Performance map is used to display the bsfc over the engines full load
and speed range. Using a dynamometer to measure the torque and fuel
mass flow rate for different throttle positions you can calculate:
bmep =
2π ⋅ T ⋅ nR
Vd
m f
bsfc =
Wb
Wb = (2π ⋅ N ) ⋅ T
bmep@WOT
Constant bsfc contours from a
2 litre four cylinder SI engine
31
Engine Efficiencies
The time for combustion in the cylinder is very short, especially at high
speeds, so not all the fuel may be consumed
A small fraction of the fuel may not react and exits with the exhaust gas
The combustion efficiency is defined as:
Qin
Q in
actual heat input
=
=
ηc =
theoretical heat input m f ⋅ QHV m f ⋅ QHV
where Qin = heat added by combustion per cycle
mf = mass of fuel added to cylinder per cycle
QHV = heating value of the fuel (chemical energy per unit mass)
32
Engine Efficiencies (2)
The thermal efficiency is defined as:
ηth =
W
W
work per cycle
=
=
heat input per cycle Qin ηc ⋅ m f ⋅ QHV
or in terms of rates
W
W
power out
=
=
ηth =
rate of heat input Q in η c ⋅ m f ⋅ QHV
Thermal efficiencies can be given in terms of brake or indicated values
Indicated thermal efficiencies are typically 50% to 60% and brake thermal
efficiencies are usually about 30%
33
Engine Efficiencies (3)
Fuel conversion efficiency is defined as:
W
W
=
ηf =
m f ⋅ QHV m f ⋅ QHV
Note: ηf is very similar to ηth, difference is ηth takes into account actual
fuel combusted.
Recall:
m f
sfc =
W
Therefore, the fuel conversion efficiency can also be obtained from:
ηf =
1
( sfc ) ⋅ QHV
34
Volumetric Efficiency
Due to the short cycle time at high engine speeds and flow restrictions
through the intake valve less than ideal amount of air enters the cylinder.
The effectiveness of an engine to induct air into the cylinders is measured
by the volumetric efficiency:
ηv =
ma
n ⋅ m
actual air inducted
=
= R a
theoretical air
ρ a ⋅ Vd ρ a ⋅ Vd ⋅ N
where ρa is the density of air at atmospheric conditions Po, To and for an
ideal gas ρa =Po / RaTo and Ra = 0.287 kJ/kg-K (at standard conditions
ρa= 1.181 kg/m3)
Typical values for WOT are in the range 75%-90%, and lower when the
throttle is closed
35
Air-Fuel Ratio
For combustion to take place the proper relative amounts of air and fuel
must be present in the cylinder.
The air-fuel ratio is defined as
AF =
ma m a
=
m f m f
For gasoline fuel the ideal AF is about 15:1, with combustion possible
in the range of 6 to 19.
For a SI engine the AF is in the range of 12 to 18 depending on the
operating conditions.
For a CI engine, where the mixture is highly non-homogeneous, the
AF is in the range of 18 to 70.
36
Relationships Between Performance Parameters
By combining equations presented in this section the following additional
working equations are obtained:
W =
η f ⋅ηv ⋅ N ⋅ Vd ⋅ QHV ⋅ ρ a ⋅ (1 / AF )
nR
η f ⋅ηv ⋅ Vd ⋅ QHV ⋅ ρ a ⋅ (1 / AF )
T=
2π ⋅ nR
mep = η f ⋅ηv ⋅ QHV ⋅ ρ a ⋅ (1 / AF )
37
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