hydraulic power system analys..., r. smith (crc, 2006) ww

8/12/2019 Hydraulic Power System Analys..., R. Smith (CRC, 2006) WW

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Chapter 3 69

must always be compared to actual operation of hydraulic power systems.Comparison will increase condence in mathematical modeling procedures.The establishment of a model will always lead to better understanding of system performance. Therefore, the time spent to write the model will bewell rewarded.

PROBLEMS

3.1 A truck with a hydraulic boom is equipped with a hydraulic chainsaw at the operators basket as shown in the gure. The pump is

mounted on the truck. The characteristics of the system are shownin the table. The temperature is constant in the system. All owvelocities in the system are equal.

Determine the power available at the motor for each of the threeelevations Z 1 , Z2 , and Z3 given on the gure.

Characteristics of a system using a movable chain saw

Characteristic Size UnitsPump displacement, D p 0.45 in.3 / revPump outlet pressure, ps 2100 lbf / in.2

Pump shaft speed 1200 rpmPressure loss between pump

and motor, p

450 lbf / in.2

Oil density, 0.03 lbm / in.3

Motor return pressure, pd 0.0 lbf / in.2

3.2 A uid power pump is used to drive a motor as shown in the gure.The components are connected with commercial steel tubing. De-

2006 by Taylor & Francis Group, LLC


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70 STEADY STATE MODELING

termine the correct pump speed, n, to provide a ow velocity, v, inthe line of 7.0 m/s. Determine the allowable torque output from themotor to provide a factor of safety of 4 for the tube wall.

PUMP

p0 p1 Q

MOTOR

DIRECTIONALCONTROLVALVE

p2 3p

Characteristics of a pump and motor transmission system

Characteristic Size UnitsTube length, L 1.2 mTube external diameter, do 12.0 mmTube wall thickness, t 0.1 mmTube tensile strength, S t 395 MPaOil viscosity, 11.5 mPa sOil density, 837 kg/ m3

Pump displacement, D p 20.0 mL/ revPump inlet pressure, p0 0.0 kPaPump volumetric efficiency,

vp95.0 %

Valve loss factor, K 10.0Motor displacement, D m 37.0 mL/revMotor mechanical efficiency,

mm94.0 %

Motor outlet pressure, p3 500 kPa

3.3 A hydraulic motor is used to drive the rear wheels of a truck througha drive shaft. The truck is equipped with an accumulator that storesthe kinetic energy of the truck during deceleration.



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Chapter 3 71

CONSTANT PRESSUREVALVE

TRUCK - MOTOR POWERS REAR WHEEL DRIVE SHAFT

CONTROLVALVE

ACCUMULATOR

MOTOR

sp rp

Determine the kinetic energy, KE, that can be stored in the accu-mulator if the truck is travelling at a velocity 70 kph and the energyis transferred to the accumulator with a pump as the truck deceler-ates to 0 kph. Determine the power, P , that is available to drivethe truck if the energy from the previous part is used in a 30 s timeinterval. Determine the acceleration of the rear wheels caused by thepressure, ps , applied to the motor. Determine the acceleration of therear wheels caused by the pressure, ps , applied to the motor when aload torque, T L , of 175 N m develops at the rear wheels. NOTE:T L is the combined load torque for both rear wheels. Determine theacceleration of the rear wheels for the conditions given in the previouspart, but with the mass of the truck, m, included in the calculation.

Simplied regenerative energy storage for a truck

Characteristic Size UnitsSystem pressure, ps 32.0 MPaMotor return pressure, pr 250.0 kPaMotor displacement, D m 55.0 mL/ revRear wheel diameter, d 900 mmTruck mass, m 1700 kgMoment of inertia, I c 20.0 kg m2

(I c is combined moment for

2 rear wheels and drive shaft)

3.4 A hydraulic lift consists of a large ram and a hand operated pump.Determine the pressure, p, and the force, F , that is needed to raisethe mass, m. Determine the power, P , that is developed to raise



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72 STEADY STATE MODELING

the mass, m, a distance, h, during the given interval. Determine thenumber of strokes required to raise the mass, m, during the interval.

Hand operated hydraulic jack system

Characteristic of item Size UnitsHand pump piston diameter,

d p0.25 in.

Hand pump piston stroke, s 5.0 in.Lifting ram piston diameter,

dr2.75 in.

Mass being lifted, m 2000 lbmHeight moved by weight, h 15.0 in.Duration of lift phase, t 4.0 min.

3.5 A hydraulic motor is used to drive the rear wheels of a truck througha drive shaft. The truck is equipped with an accumulator that storesthe kinetic energy of the truck during deceleration.

CONSTANT PRESSURE

VALVE

TRUCK - MOTOR POWERS REAR WHEEL DRIVE SHAFT

CONTROL

VALVE

ACCUMULATOR

MOTOR

sp rp

Determine the kinetic energy, KE, that can be stored in the accumu-



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Chapter 3 73

lator if the truck is travelling at a velocity 45 mph and the energyis transferred to the accumulator with a pump as the truck deceler-ates to 0 mph. Determine the power, P , that is available to drivethe truck if the energy from the previous part is used in a 30 s timeinterval. Determine the acceleration of the rear wheels caused by thepressure, ps , applied to the motor. Determine the acceleration of therear wheels caused by the pressure, ps , applied to the motor when aload torque, T L , of 1550 lbf in. develops at the rear wheels. NOTE:T L is the combined load torque for both rear wheels. Determine theacceleration of the rear wheels for the conditions given in the previouspart , but with the mass of the truck, m, included in the calculation.

Simplied regenerative energy storage for a truck

Characteristic Size UnitsSystem pressure, ps 4500 lbf / in.2

Motor return pressure, pr 50 lbf / in.2

Motor displacement, D m 3.4 in.3 / revRear wheel diameter, d 35.0 in.Truck mass, m 3800 lbmMoment of inertia, I c 177 lbf in. s2

(I c is combined moment for2 rear wheels and drive shaft)

3.6 A uid power pump is used to drive a motor as shown in the gure.The ow velocity equals the line velocity thus v1 = v2 = v3 = v4 .

Determine the Reynolds Number, Re, uid friction pressure loss, pf ,and the valve geometry loss, pk , in the ow line between stations 2and 3. Determine the power, P m , produced by the motor. Determinethe heat ow, Qh J/h, that must be removed between stations 1 and4 to maintain the nal temperature, 4 .



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74 STEADY STATE MODELINGHeat generation in a pump and motor transmission system

Characteristic Size UnitsPump power input, P p 20 kWPump inlet pressure, p1 0Pump outlet pressure, p2 17.0 MPaPump inlet oil temperature,

185.0 C

Valve loss factor, K 200

Total line length, L 8.0 mLine diameter, d 30.0 mmMotor outlet pressure, p4 0 PaMotor outlet temperature, 4 85.0 C Oil specic heat, C p 2002 J/ kg COil density, 850 kg/ m3

Oil viscosity, 9.4 mPa s

3.7 A uid power pump is used to drive a cylinder as shown in the gure.

Determine the uid friction pressure loss, pf , and the valve losses, pvp and pvr . Determine the required pressure, p, at the piston todrive the cylinder. Determine the required pump speed, n rpm.



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Chapter 3 75Characteristics of a pump and cylinder system

Characteristic Size UnitsCylinder piston diameter,

d p42.0 mm

Cylinder rod diameter, dr 20.0 mmCylinder load force, F 17000 NPiston velocity, y 0.35 m/sPump displacement, D p 32.0 mL/rev

Pump volumetric efficiency,V 95 %

Line length, L 4.0 mLine diameter, d 12.0 mmFlow coefficient into cylinder,

C dp0.60

Flow coefficient for return,C dr

0.62

Valve ow area into cylinder,Avp

15.0 mm 2

Valve ow area for return, Avr 17.0 mm2

Oil mass density, 850 kg/ m3

Oil viscosity, 9.4 mPa s

REFERENCES

1. Merritt, H. E. , 1967, Hydraulic Control Systems , John Wiley & Sons,New York, NY.

2. Paul-Munroe Rucker, Inc., 1994, Fluid Power Designers Lightning Reference Handbook , 8th ed., Paul-Munroe Rucker, Inc., Whittier,

CA.

3. Munson, B. R., Young, D. F., and Okiishi, T. H., 1994, Fundamentals of Fluid Mechanics , 2nd ed., John Wiley & Sons, New York, NY.

4. Blackburn, J. F., Reethof, G., and Shearer, J. L., 1960, Fluid Power Control , The M.I.T. Press, Cambridge, MA.


hydraulic power system analys..., r. smith (crc, 2006) ww

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