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II-C Power & Energy Systems Dennis Buckmaster dbuckmas@purdue.edu https://engineering.purdue.edu/~dbuckmas/ dbuckmas@purdue.edu OUTLINE Internal combustion engines Hydraulic power circuits Mechanical power transmission Electrical circuit analysis (briefly)

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References Engineering Principles of Agricultural Machinery, 2 nd ed. 2006. Srivastava, Goering, Rohrbach, Buckmaster. ASABE. Off-Road Vehicle Engineering Principles. 2003. Goering, Stone, Smith, Turnquist. ASABE.

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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.

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Engines Power and Efficiencies Thermodynamics Performance

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Engine Power Flows

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Power & Efficiencies Fuel equivalent P fe,kW = (Hg kJ/kg 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 = 2πT Nm N e,rpm /60000 Friction P f = P i -P b

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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

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Dual Cycle

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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 [n = 1 (isothermal) to 1.4 (adiabatic), about 1.3 during compression & power strokes]

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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

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What is the displacement of a 6 cylinder engine having a 116 mm bore and 120 mm stroke?

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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?

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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)

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17 A quick problem … Diesel engine generating 60 kW at 2300 rpm Q: torque available

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Power Hydraulics Principles Pumps, motors Cylinders

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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

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20 Liquids Have no Shape of their own

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21 Liquids are Practically Incompressible

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Pascals 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

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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

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24 Hydraulic lever

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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)

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26 Trapped Oil Closed Center HydraulicsOpen Center Flow in Neutral

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Extend 27

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Retract 28

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Neutral Again 29

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Pumps

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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

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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

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Speed Flow Q gpm = D cu in/rev N rpm /231

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Pressure Rise Torque Required T inlb = D cu in/rev P psi /(2π)

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Pressure Flow Theoretical pump Effect of leakage Relief valve or pressure compensator

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Pressure Flow Constant power curve P hp = P psi Q gpm /1714

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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

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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?

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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

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Example motor problem If a motor with 2 in 3 /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 its overall efficiency? c. How fast will it turn? d. How much torque will be generated?

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Cylinders Force balance on piston assembly: F external P 1 * A 1 P 2 * A 2

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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

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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

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Power Transmission

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Transmissions transform power a torque for speed tradeoff

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Gears

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Planetary Gear Sets

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Belt & Chain Drives Speed ratio determined by sprocket teeth or belt sheave diameter ratio

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FIRST GEAR

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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

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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

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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

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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 P hp = T ft-lb N rpm /5252

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Electricity Voltage = Current * Resistance V volts = I amps * R ohms Power = voltage times current P Watts = V volts *I amps V IR

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Three Types of Circuits Series Same current, voltage divided + - 12 v. Parallel Same voltage, current divided Series / Parallel

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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

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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

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Good luck on the PE Exam! My email address: 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

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