II-C Power & Energy Systems Dennis Buckmaster [email protected] dbuckmas/ [email protected] OUTLINE Internal combustion.

II-C Power & Energy SystemsDennis Buckmaster

[email protected]://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]

• 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

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/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)

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

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

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 Principles1 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 HydraulicsOpen CenterFlow 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

• 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

Speed

Flow

Qgpm = Dcu in/rev Nrpm /231

Pressure Rise

TorqueRequired

Tinlb = Dcu in/rev ∆Ppsi /(2π)

Pressure

Flow

Theoretical pump

Effect of leakage

Relief valve or pressure compensator

Pressure

Flow

Constant power curve

Php = Ppsi Qgpm/1714

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

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 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 pump problems

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: Fexternal

P1 * A1P2 * A2

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 powera 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 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 the driven shaft receive?

Example belt problem

Php = Tft-lbNrpm/5252

ElectricityElectricity

Voltage = Current * Resistance

Vvolts = Iamps * Rohms

Power = voltage times current

PWatts = Vvolts*Iamps

V

I R

Three Types of CircuitsThree 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!

• My email address:

[email protected]

• My web page:

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

Note … ASABE members can access ASABE texts electronically at:

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