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TEP4205 INDUSTRIAL HYDRAULICS

P Chapple February 2005. Tutorial Questions 2

3)

The volumetric efficiency of a hydraulic pump is 97.5% and its mechanical efficiency is 90% when

it is operating at 1450 rev/min and the delivery pressure is 100 bar. At this condition the viscousfriction and coulomb friction torque losses are equal.

Calculate the variation of the losses as a function of pressure and hence obtain values of overallefficiency for delivery pressures ranging from 0 to 200 bar. Determine the maximum overallefficiency.

(88.1%)

Question based on Chapter 8

4)

The hydraulic circuit shown in Figure 1 is a simple move and press circuit with two linear actuatorscontrolled by two directional control valves. A fixed displacement pump having a relief valve to limitthe maximum system pressure supplies hydraulic fluid. The circuit is designed such that the pressactuator can only be activated when the move actuator is held in the fully extended position.

Figure 2 illustrates how this system could have been installed in the factory. It is required to select asuitable pipe diameter, and to estimate the resulting pressure loss between the pump and the inlet tothe piston end of the move actuator under normal operating conditions. Use the graphical datagiven in Figures 4 - 6. The DArcy equation for the pressure drop is:

2 U

d L

4f = p2 where L is the equivalent length of the pipe including the allowance

for pipe fittings and bends.

Note It is usual to aim at a mean fluid velocity of 5ms -1, which can be used to determine an initialdiameter for the pipe for a first calculation.

System properties:Fluid 32 Grade mineral oil (32 cSt at 40 0C)

Temperature 50 CPressure 100 barPump flow 60 L min -1

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Figure 1 Move and press hydraulic circuit.

Figure 2 Installation diagram.

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Figure 3 Resistance of Valve Ports.

Figure 4 Oil Viscosity Variation with Temperature

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Figure 6 Moody Diagram for Pipe Friction Factors

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5)

a) For the circuit shown in Figure 1, it is required to determine the size of the restrictor ( as a

rated flow) that is to be used during extension of the actuator. For the data given calculate therated flow of the restrictor valve (L/min) at a rated pressure drop of 10bar that will provide thespecified actuator velocity. ( 19L/min)

Figure 1 Actuator CircuitData

Opposing force on the actuator rod = 20 kN Actuator velocity = 0.5 ms -1 Actuator piston diameter = 50 mm Actuator rod diameter = 25 mmRelief valve set pressure (P smax ) = 200 barPump flow = 80 L/minThe pressure in the return line from the actuator can be assumed to be zero.

b) Show how the circuit can be modified in order that the extending actuator velocity will be

controlled when the force is negative (pulling).

c) In order to prevent the actuator velocity changing with changes in the load force a pressurecompensated flow control valve can be used in place of the restrictor valve. Draw a sketch of thistype of valve and briefly describe its method of operation.

P SQS P T

P S A B

P P QP

P smax

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Question based on Chapter 7, 5.4

6)

i) A four-way spool valve is used to position a hydraulic actuator with a supply pressure of 250 bar.The valve spool is a fully annular design of 6 mm diameter, with a maximum movement of 0.5 mmand C q = 0.62.

For a double ended actuator (equal area) having areas of 12.5 cm 2 calculate the maximum powerwhich can be transmitted to the actuator and its speed and thrust at this condition.

(20.8 x 10 3 N, 0.46m/s, 9.6 kW )

ii) For an unequal area actuator with zero force conditions show that the ratio of extension velocity(uE) to retraction velocity (u R) is given by:

E

R

u Au A

= 12

iii) For an unequal area actuator having areas of 12.5 and 25 cm 2 respectively, and using the valveand supply pressure in i) calculate the thrust and actuator pressures when extending at 0.49 ms -1.

(58bar, 48bar, 8.5kN ) 7)

Questions based on Chapters 3 and 7

It is required to select an actuator, which is pin jointed at both ends and mounted horizontally, tomove a load as described in the data. Using the data sheet in Table 1 for a range of availableactuators having different mounting methods, select an actuator that will provide the necessarystroke length and required stall force for the extension of the actuator.

P S

Q1 Q 2 P 1 P 2

A2 A1Velocity U E

Force F

A B

P T

= A 1 /A2 Rod for equalarea actuator

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Calculate the actuator pressures and flows for the given load duty condition and determine therated flow for a valve rated total pressure drop of 70 bar (35 bar across each valve metering edge,or land).

(case 3 & 4 at 100bar 860mm, case 3, 82bar, 4.3bar,131L/min )

Table 1 Actuator Data

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Load Data

Maximum stall force 31000 N

Actuator stroke 800 mm

Load operating condition

Force = 25000 N at 0.5 m/s velocity.

8)

A four-way spool valve is used to control a hydraulic motor operating against a steady load with asupply pressure of 140 bar.

The valve has fully annular ports with a spool of 12.5mm diameter, which is opened by 1.25 mm.

The motor has a displacement of 64 cm 3/rev, with a mechanical efficiency 90% and a volumetricefficiency of 95%. For a load torque of 32 Nm. calculate the motor speed and the overallefficiency of the system.

(2980 rev/min, 21.4%)

9)

Question based on Chapters 5 and 7 and worked example No. 10

Figure 1 shows a weight-loaded actuator that is operated by a central bypass type of open centrevalve. The actuator ports are connected together so that the piston and annulus pressures arealways equal and the rod area determines the actuator velocity (i.e. the inlet flow from the valve =the piston flow the annulus flow)

a) For the given data tabulate, or plot graphically, the relationship between the actuatorvelocity and pump pressure with the valve position for zero actuator load force.

(max velocity = 1.72 m/s, at x = 6mm and zero at x = 2mm)b) For a valve opening of 5mm determine the stalled actuator load and the maximum possible

actuator velocity.(136.2kN and 1.29m/s from a))

c) For the valve opening in b) estimate the actuator force when the flow from the outlet port Aof the valve is 100 and 200 L/min respectively.

(76kN, 30kN) Describe the purpose of the check valve shown in Figure 1.

(to prevent load reversal)

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Data

Pump flow = 400 L/minValve spool diameter ( d ) = 12 mmCentral bypass opening for valve in central position ( L) = 6 mmValve overlap at port A ( x 0 ) = 2 mm

Actuator rod diameter = 70 mm Actuator piston diameter = 100 mm

10)

Question based on Chapter 6

a) Show that the volume that can be discharged from a gas type accumulator is given by thefollowing equation:

V

1P P

P P

V 1

1

2

0

2

0

=

p0 is the precharge pressureV0 is the stored volume at the precharge pressureP 1 is the minimum pressure required for operation of the systemP 2 is the maximum required pressure

Assume that the gas is compressed isothermally from P 0 to P 2 and expands adiabatically from P 2 to P 1 with the adiabatic index .

b) A hydraulic actuator is required to perform 60 cycles per hour, each cycle requiring 0.9litres of oil to operate the actuator in a time of 8s. A fixed displacement pump supplies 1 litre/min to

the system the outlet pressure of which is controlled by a relief valve at a pressure of 100 bar.

Figure 1 Valve control of aweight loaded actuator

A

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Determine the volumetric capacity of the accumulator that is required to operate the system at aminimum pressure of 75 bar. The precharge pressure is set at 90% of the minimum pressure andthe adiabatic index to be used is 1.6.

(5.6L)

Question based on Chapters 2, 7, 8, and 9.

11)

A closed loop hydrostatic transmission system is to be used to drive the tracks of an excavator forwhich there are two motors, each one being used to drive a track as shown in the Figure 1.

Figure 1 Excavator track drive

a) Using the given data calculate the motor torque required to start moving the excavator upan incline of 20 0 and the motor speed required to drive the excavator on level ground at maximumspeed. Use these values to select a suitable motor type from the table that will provide therequired performance.

(288rev/min, B)b) Calculate:

i. The maximum flow from each pump that is required to drive the selected motors. ( 25L/min) ii. The maximum displacement of each pump. ( 14.6 cm 3 /rev) iii. The pump pressure and the total input power to the pump that are required to drive the

excavator at the maximum speed on level ground. ( 144bar, 6.65kW)

c) Calculate the maximum speed when using a hydraulic fluid having a viscosity of 20 cSt.(268rev/min)

d) Sketch a circuit for the hydrostatic system, which includes:

Relief valves for limiting the maximum circuit pressure

Brake control valves The method for supplying boost flow into the circuit.

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e)

It is intended to use variable displacement motors for the excavator track drive system. Calculate

the minimum value of motor displacement that can be used to drive the excavator on level groundat the maximum motor flow from b) i) at the maximum pressure of 210bar .

(67.8cm 3 /rev)

Data

Total weight 5400N Maximum speed (U max ) 6m/s Static friction force to start moving the excavator 450N Friction force at speeds > 0 250 + 250U (U = velocity m/s ) NTrack drive wheel diameter 0.4m

Motor mechanical efficiency 85% for starting at zero speed ( MS )

92% for motor speeds greater than zero ( MD ).

Pump and motor volumetric efficiencies 95% (with a hydraulic fluid viscosity of 32centistoke cSt ) PV MV ( , )

Pump mechanical efficiency 95% ( PM )

Pump speed 1800 rev/min (N )Maximum pressure 210 bar ( max P )

Motor Data

Motor type Theoretical displacement(cm 3 /rev)

Maximum speed(rev/min)

A 102 250 B 83 300C 67 350

12)

Question from Chapter 6

Figure 1 Pump and motor system

A

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Data

Torque required at maximum motor speed 175Nm

Motor displacement 82cm3

/rev (D M )Motor mechanical efficiency 92% for motor speeds greater than zero ( MM ).

Motor volumetric efficiency 93% MV ( )

Pump mechanical efficiency 95% ( PM )

Pump volumetric efficiency 96% PV ( )

Pump speed 1800rev/min (N P )Pump displacement 15cm 3 /rev (D P )Fluid specific heat 2100J/kg/ 0 C (C P ) Heat dissipated in the cooler for a water

inlet temperature of 20 0 C OW

T kW

3 40

( OW T is the difference between the cooler oil inlet and water inlet temperatures).Pump external drain leakage flow = 50% of the total pump leakage

a) For operating the motor against the stated torque that is required at the maximum motorspeed calculate:

1) The pressure required at the motor inlet.2) The pump outlet flow.3) The motor speed at this operating condition.4) The flow at the cooler inlet (point A in Figure 2).

b) Assuming that all of the volumetric and mechanical losses are dissipated into the hydraulicsystem fluid and that there is no heat transfer from the fluid to the environment through the pipescalculate:

1) The total heat generated by the losses.2) The temperature increase in the hydraulic fluid between the pump inlet and the cooler

inlet assuming that there is perfect mixing of the flows at point A.

3) The temperature of the hydraulic fluid at the cooler inlet (point A) that is required to

dissipate the heat that is generated in 1). (Note that the heat extracted from the fluid in the cooleris dependent on the difference ow T between the temperatures of the hydraulic fluid at the coolerinlet and the cooling water inlet).

4) The reduction in the fluid temperature through the cooler and the temperature in thereservoir.

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