II-C Power & Energy Systems
Dennis Buckmaster
dbuckmas@purdue.edu
https://engineering.purdue.edu/~dbuckmas/
OUTLINE
• Internal combustion engines
• Hydraulic power circuits
• Mechanical power transmission
• Electrical circuit analysis (briefly)
References
• Engineering Principles of
Agricultural Machinery, 2nd
ed. 2006. Srivastava,
Goering, Rohrbach,
Buckmaster. ASABE.
• Off-Road Vehicle
Engineering Principles.
2003. Goering, Stone, Smith,
Turnquist. ASABE.
Other good sources
• Fluid Power Circuits and
Controls: Fundamentals
and Applications. 2002.
Cundiff. CRC Press.
• Machine Design for
Mobile and Industrial
Applications. 1999. Krutz,
Schueller, Claar. SAE.
Engines
• Power and Efficiencies
• Thermodynamics
• Performance
Engine Power Flows
Power &
Efficiencies
• Fuel equivalent
Pfe,kW = (HgkJ/kg∙ṁf,kg/h)/3600
[Hg = 45,000 kJ/kg for No. 2 diesel]
• Indicated
Pi,kW = pime,kPaDe,lNe,rpm/120000
• Brake
Pb,kW = 2πTNmNe,rpm/60000
• Friction
Pf = Pi-Pb
Power &
Efficiencies
• Indicated Thermal
Eit = Pi/Pfe
• Mechanical
Em = Pb/Pi
• Overall (brake thermal)
Ebt = Pb/Pfe = Eit*Em
• Brake Specific Fuel Consumption
BSFC= ṁf,kg/h/Pb,kW
Dual Cycle 
Related equations
• Compression ratio = r
r = V1/V2
• Displacement
De,l = (V1-V2)*(# cylinders)
= π(borecm)2(strokecm)*(# cyl)/4000
• Ideal gas
p1V1/T1 = P2V2/T2
• Polytropic compression or expansion
p2/p1 = rn
[n = 1 (isothermal) to 1.4 (adiabatic), about 1.3 during
compression & power strokes]
Related equations
• Air intake
ṁa,kg/h = .03De,lNe,rpmρa,kg/cu mηv,decimal
From Stoichiometry (fuel chemistry)
• A/F = air to fuel mass ratio = 15:1 for cetane
What is the displacement of a 6 cylinder
engine having a 116 mm bore and 120 mm
stroke?
For this same engine (7.6 l displacement, 2200 rpm rated speed), what is the air
consumption if it is naturally aspirated and has a volumetric efficiency of 85%?
Assume a typical day with air density of 1.15 kg/m3.
With a stoichiometric air to fuel ratio based on cetane, at what rate could fuel
theoretically be burned?
Consider the this same (595 Nm, 137 kW @ 2200 rpm) engine which has a high
idle speed of 2400 rpm and a torque reserve of 30%; peak torque occurs at 1300
rpm. Sketch the torque and power curves (versus engine speed).
Torque (Nm)
Power (kW)
Speed (rpm)
A quick problem …
• Diesel engine generating 60 kW at 2300 rpm
• Q: torque available
17
Alternative fuels
What has to be similar?
• Self Ignition Temperature
• Energy density
• Flow characteristics
• Stoichiometric A/F ratio
Power Hydraulics
• Principles
• Pumps, motors
• Cylinders
About Pressure
• 14.7 psia STP (approx __ in Hg)
• Gage is relative to atmospheric
• Absolute is what it says … absolute & relative to
perfect vacuum
• What causes oil to enter a pump?
• Typical pressures:
– Pneumatic system
– Off-road hydraulic systems
20
Liquids Have no Shape of their own
21
Liquids are
Practically Incompressible
22
Pascal’s Law
• Pressure Exerted on a Confined Fluid is
Transmitted Undiminished in All Directions
and Acts With Equal Force on Equal Areas
and at Right Angles to Them.
23
Application Principles
1 lb (.45kg)
Force
10 lbs (4.5kg)
10 sq in
(6.5cm2)
Piston Area
1 sq in (.65cm2)
Piston Area
1 psi
(6.9kpa)
24
Hydraulic “lever”
25
Types of Hydraulic Systems
Open Center
Closed Center
The control valve that regulates the flow from the pump
determines if system is open or closed.
Do not confuse Hydraulics with the “Closed Loop” of the
Power Train. (Hydro)
26
ClosedOpen
Center
Center
Hydraulics
Flow in Neutral
Trapped Oil
27
Extend
28
Retract
29
Neutral Again
30
Pumps
Pump Inefficiency
• Leakage: you get less flow from a pump
than simple theory suggests.
– Increases with larger pressure difference
• Friction: it takes some torque to turn a
pump even if there is no pressure rise
– Is more of a factor at low pressures
Efficiency of pumps & motors
• Em – mechanical efficiency < 1 due to
friction, flow resistance
• Ev – volumetric efficiency < 1 due to
leakage
• Eo =overall efficiency = Em * Ev
• Eo = Power out/power in
Qgpm = Dcu in/rev Nrpm /231
Flow
Speed
Tinlb = Dcu in/rev ∆Ppsi /(2π)
Torque
Required
Pressure Rise
Theoretical pump
Effect of leakage
Flow
Relief valve or pressure
compensator
Pressure
Constant power curve
Flow
Pressure
Php = Ppsi Qgpm/1714
Example pump
problems
1a. If a pump turns at
2000 rpm with a
displacement of 3
in3/rev, theoretically,
how much flow is
created?
1b. If the same pump is
95% volumetrically
efficient (5%
leakage), how much
flow is created?
Example pump
problems
2a. If 8 gpm is required
and the pump is to turn
at 1750 rpm, what
displacement is
theoretically needed?
2b. If the same pump will
really be is 90%
volumetrically efficient
(10% leakage), what is
the smallest pump to
choose?
Example pump
problems
3a. A 7 in3/rev pump is to
generate 3000 psi
pressure rise; how much
torque will it theoretically
take to turn the pump?
3b. If the same pump is
91% mechanically
efficient (9% friction &
drag), how much torque
must the prime mover
deliver?
Example motor
problem
If a motor with 2 in3/rev
displacement and 90%
mechanical and 92%
volumetric efficiencies
receives 13 gpm at
2000 psi …
a. How much fluid power
is received?
b. What is it’s overall
efficiency?
c. How fast will it turn?
d. How much torque will
be generated?
Cylinders
Force balance on
piston assembly:
P1 * A1
P2 * A2
Fexternal
Example cylinder
problem
• 3000 psi system
• 2” bore cylinder
• Extends 24 inches in 10
seconds
• Q: max force generated
•
max work done
•
power used
•
flow required
43
• Tractor source with 2500 psi
Example cylinder and 13 gpm available
problem
• Return pressure “tax” of 500 psi
• Cylinder with 3” bore, 1.5” rod
diameters
• Q1: How much force will the
cylinder generate?
• Q2: How long will it take to
extend 12 inches?
Power Transmission
Transmissions transform power
a torque for speed tradeoff
Gears
Planetary Gear Sets
Belt & Chain Drives
• Speed ratio determined by sprocket teeth
or belt sheave diameter ratio
FIRST GEAR
FIRST GEAR
First gear speeds … if … Input shaft: 1000 rpm
Main countershaft: 1000 (22/61) = 360 rpm
Ratio = input speed/output speed = 1000/360 = 2.78
Ratio = output teeth/input teeth = 61/22 = 2.78
Secondary countershaft: 360 rpm (41/42) = 351 rpm
Output shaft: 351 rpm (14/45) = 109 rpm
RATIO: input speed/output speed = 1000/109 = 9.2
Product of output teeth/input teeth = (61/22)(42/41)(45/14) = 9.2
Example gear
problem
• If 50 kW @ 2400 rpm drives a
pinion gear with 30 teeth and
the meshing gear has 90
teeth (assume 98%
efficiency)…
• Q1: What is the speed of the
output shaft?
• Q2: How much power leaves
the output shaft?
• Q3: How much torque leaves
the output shaft?
Example planetary If the sun of a planetary gear
set turns at 1000 rpm, what
gear problem
speed of the ring would
result in a still planet
carrier? Teeth on gears are
sun: 20 and ring: 100.
Example belt
problem
If a belt drive from a 1750 rpm
electric motor is to transmit
5 hp to a driven shaft at 500
rpm and the small sheave
has a pitch diameter of 4” …
Q1: What should the pitch
diameter of the other pulley
be?
Q2: Which shaft gets the small
sheave?
Q3: How much torque does
the driven shaft receive?
Php = Tft-lbNrpm/5252
Electricity
Voltage = Current * Resistance
Vvolts = Iamps * Rohms
V
I R
Power = voltage times current
PWatts = Vvolts*Iamps
Three Types of Circuits
Series
Same current, voltage divided
Parallel
Same voltage, current divided
Series / Parallel
+
12 v.
-
Example 12 V DC A 12 V DC solenoid a
hydraulic valve has a 5 amp
problem
fuse in its circuit.
Q1: What resistance would
you expect to measure as
you troubleshoot its
condition?
Q2: How much electrical
power does it consume?
Example 12 V DC Q1: Identify specifications for
a relay of a 12 V DC lighting
problem
circuit on a mobile machine
if the circuit has four 60W
lamps.
Q2: Would the lamps be wired
in series or parallel?
Good luck on the PE Exam!
• My email address:
dbuckmas@purdue.edu
• My web page:
https://engineering.purdue.edu/~dbuckmas/
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