# II-C Power & Energy Systems

Mechanics

Oct 27, 2013 (4 years and 8 months ago)

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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, 2
nd

ed.

2006. Srivastava,
Goering, Rohrbach,
Buckmaster. ASABE.

Off
-
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

P
fe,kW

= (Hg
kJ/kg
∙ṁ
f,kg/h
)/3600

[Hg = 45,000 kJ/kg for No. 2 diesel]

Indicated

P
i,kW

= p
ime,kPa
D
e,l
N
e,rpm
/120000

Brake

P
b,kW

= 2
π
T
Nm
N
e,rpm
/60000

Friction

P
f

= P
i
-
P
b

Power &
Efficiencies

Indicated Thermal

E
it

= P
i
/P
fe

Mechanical

E
m

= P
b
/P
i

Overall (brake thermal)

E
bt

= P
b
/P
fe

= E
it
*E
m

Brake Specific Fuel Consumption

BSFC=

f,kg/h
/P
b,kW

Dual Cycle

Related equations

Compression ratio = r

r = V
1
/V
2

Displacement

D
e,l

= (V
1
-
V
2
)*(# cylinders)

=
π
(bore
cm
)
2
(stroke
cm
)*(# cyl)/4000

Ideal gas

p
1
V
1
/T
1

= P
2
V
2
/T
2

Polytropic compression or expansion

p
2
/p
1

= r
n

compression & power strokes]

Air intake

a
,kg/h

= .03D
e,l
N
e,rpm
ρ
a,kg/cu m
η
v,decimal

From Stoichiometry (fuel chemistry)

A/F = air to fuel mass ratio = 15:1 for cetane

Related equations

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/m
3
.

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)

Speed (rpm)

Power (kW)

17

A quick problem …

Diesel engine generating 60 kW at 2300 rpm

Q: torque available

Power Hydraulics

Principles

Pumps, motors

Cylinders

19

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
-

20

Liquids Have no Shape of their own

21

Liquids are

Practically Incompressible

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.

22

Application Principles

1 lb (.45kg)

Force

1 sq in (.65cm2)

Piston Area

1 psi

(6.9kpa)

10 sq in
(6.5cm2)

Piston Area

10 lbs (4.5kg)

23

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

Trapped Oil

Closed Center Hydraulics

Open Center

Flow in Neutral

Extend

27

Retract

28

Neutral Again

29

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

E
m

mechanical efficiency < 1 due to
friction, flow resistance

E
v

volumetric efficiency < 1 due to
leakage

E
o

=overall efficiency = E
m

* E
v

E
o

= Power out/power in

Speed

Flow

Q
gpm

= D
cu in/rev

N
rpm

/231

Pressure Rise

Torque

Required

T
inlb

= D
cu in/rev

∆P
psi

/(2
π
)

Pressure

Flow

Theoretical pump

Effect of leakage

Relief valve or pressure
compensator

Pressure

Flow

Constant power curve

P
hp

= P
psi

Q
gpm
/1714

1a. If a pump turns at
2000 rpm with a
displacement of 3
in
3
/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

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?

3a. A 7 in
3
/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 pump
problems

Example motor
problem

If a motor with 2 in
3
/rev
displacement and 90%
mechanical and 92%
volumetric efficiencies
2000 psi …

a. How much fluid power

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:

F
external

P
1

* A
1

P
2

* A
2

42

3000 psi system

2” bore cylinder

Extends 24 inches in 10
seconds

Q: max force generated

max work done

power used

flow required

Example cylinder
problem

Tractor source with 2500 psi
and 13 gpm available

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?

Example cylinder
problem

Power Transmission

Transmissions transform power

Gears

Planetary Gear Sets

Belt & Chain Drives

Speed ratio determined by sprocket teeth
or belt sheave diameter ratio

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

FIRST GEAR

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 gear
problem

If the sun of a planetary gear
set turns at 1000 rpm, what
speed of the ring would
result in a still planet
carrier? Teeth on gears are
sun: 20 and ring: 100.

Example planetary
gear 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

Example belt
problem

P
hp

=
T
ft
-
lb
N
rpm
/5252

Electricity

Voltage = Current * Resistance

V
volts

= I
amps

* R
ohms

Power = voltage times current

P
Watts

= V
volts
*I
amps

V

I

R

Three Types of Circuits

Series

Same current, voltage divided

+

-

12 v.

Parallel

Same voltage, current divided

Series / Parallel

A 12 V DC solenoid a
hydraulic valve has a 5 amp
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
problem

Q1: Identify specifications for
a relay of a 12 V DC lighting
circuit on a mobile machine
if the circuit has four 60W
lamps.

Q2: Would the lamps be wired
in series or parallel?

Example 12 V DC
problem

Good luck on the PE Exam!

dbuckmas@purdue.edu

My web page:

https://engineering.purdue.edu/~dbuckmas/

Note … ASABE members can access ASABE
texts electronically at:

http://asae.frymulti.com/toc.asp