Download Probsfor TEP4195 130..

TEP4195 TURBOMACHINERY
TUTORIAL QUESTIONS FOR COURSE TEP 4195
Data:
Hydraulic Oil Density
Absolute viscosity
Spool valve discharge coefficient
870 kg/m3
0.03 Ns/m2
0.62.
1)
A hydrostatic transmission has a variable displacement axial-piston pump, with a maximum
displacement of 12 cm 3/rev, and a fixed capacity motor of 120cm 3/rev displacement. The motor
speed is 138 rev/min when driving a load torque of 200Nm and when the pump is set to maximum
displacement and driven at a speed of 1450 rev/min.
Note
This information enables the value of the total leakage and volumetric efficiency to be determined
by calculating the ideal pump flow and motor speed. The total leakage is assumed to be
proportional to the pressure.
If the load is increased to 400 Nm and the pump control set to 50% maximum capacity, estimate:
(a)
the steady state speed of the motor
(58.5 rev/min)
(b)
the input power to the pump and the overall efficiency
(3.6 kW, 69%)
The pump mechanical efficiency is 95% at full stroke and 90% at half stroke.
mechanical efficiency is 95%.
The motor
2)
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 the
rated flow of the restrictor valve (L/min) at a rated pressure drop of 10bar that will provide the
specified actuator velocity.
(19L/min)
P Chapple April 2006.
Tutorial Questions
1
TEP4195 TURBOMACHINERY
PP
QP
PS
A
PS
QS
P
B
T
Psmax
Figure 1 Actuator Circuit
Data
Opposing force on the actuator rod
= 20 kN
Actuator velocity
= 0.5 ms-1
Actuator piston diameter
= 50 mm
Actuator rod diameter
= 25 mm
Relief valve set pressure (Psmax)
= 200 bar
Pump flow
= 80 L/min
The 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 pressure
compensated flow control valve can be used in place of the restrictor valve. Draw a sketch of this
type of valve and briefly describe its method of operation.
A2
A1
3)
Velocity UE
Force F
Q1
P1
Rod for equal
area actuator
Q2
P2
A
B
P
Ps
T
 = A1 /A2
PS
P Chapple April 2006.
Tutorial Questions
2
TEP4195 TURBOMACHINERY
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 mm
and Cq = 0.62.
For a double ended actuator (equal area) having areas of 12.5 cm2 calculate the maximum power
which can be transmitted to the actuator and its speed and thrust at this condition.
(20.8 x 103 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 (uR) is given by:
uE

uR
A1
A2
iii) For an unequal area actuator having areas of 12.5 and 25 cm2 respectively, and using the valve
and supply pressure in i) calculate the thrust and actuator pressures when extending at 0.49 ms-1.
(58bar, 48bar, 8.5kN)
4)
Question based on Chapter 6
a)
Show that the volume that can be discharged from a gas type accumulator is given by the
following equation:
V0 
 P2

P
 0

 P2

 P1



1







 1

V
p0 is the precharge pressure
V0 is the stored volume at the precharge pressure
P1 is the minimum pressure required for operation of the system
P2 is the maximum required pressure
Assume that the gas is compressed isothermally from P0 to P2 and expands adiabatically from P2
to P1 with the adiabatic index .
b)
A hydraulic actuator is required to perform 60 cycles per hour, each cycle requiring 0.9
litres 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.
Determine the volumetric capacity of the accumulator that is required to operate the system at a
minimum pressure of 75 bar. The precharge pressure is set at 90% of the minimum pressure and
the adiabatic index to be used is 1.6.
(5.6L)
P Chapple April 2006.
Tutorial Questions
3
TEP4195 TURBOMACHINERY
5)
A closed loop hydrostatic transmission system is to be used to drive the tracks of an excavator for
which 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 up
an incline of 200 and the motor speed required to drive the excavator on level ground at maximum
speed. Use these values to select a suitable motor type from the table that will provide the
required performance.
(288rev/min, B)
b)
Calculate:
i.
ii.
iii.
c)
d)
The maximum flow from each pump that is required to drive the selected motors. (25L/min)
The maximum displacement of each pump.
(14.6 cm3/rev)
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)
Calculate the maximum speed when using a hydraulic fluid having a viscosity of 20 cSt.
(268rev/min)
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.
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 ground
at the maximum motor flow from b) i) at the maximum pressure of 210bar.
(67.8cm3/rev)
P Chapple April 2006.
Tutorial Questions
4
TEP4195 TURBOMACHINERY
Data
Total weight
5400N
Maximum speed (Umax)
6m/s
Static friction force to start moving the excavator 450N
Friction force at speeds > 0
250 + 250U (U = velocity m/s) N
Track drive wheel diameter
0.4m
85% for starting at zero speed ( MS )
Motor mechanical efficiency
92% for motor speeds greater than zero ( MD ).
Pump and motor volumetric efficiencies
95% (with a hydraulic fluid viscosity of 32
centistoke cSt) (PV , MV )
Pump mechanical efficiency
95% ( PM )
Pump speed
1800 rev/min (N)
Maximum pressure
210 bar ( Pmax )
Motor Data
Motor type
A
B
C
Theoretical displacement
(cm3/rev)
102
83
67
Maximum speed
(rev/min)
250
300
350
6)
A
Figure 1 Pump and motor system
Data
Torque required at maximum motor speed
Motor displacement
175Nm
82cm3/rev (DM)
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 )
P Chapple April 2006.
Tutorial Questions
5
TEP4195 TURBOMACHINERY
Pump speed
Pump displacement
Fluid specific heat
Heat dissipated in the cooler for a water
TOW
kW
40
is the difference between the cooler oil inlet and water inlet temperatures).
inlet temperature of 200C
( TOW
1800rev/min (NP)
15cm3/rev (DP)
2100J/kg/0C (CP)
Pump external drain leakage flow
3
= 50% of the total pump leakage
a)
For operating the motor against the stated torque that is required at the maximum motor
speed 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 hydraulic
system fluid and that there is no heat transfer from the fluid to the environment through the pipes
calculate:
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 cooler
is dependent on the difference Tow between the temperatures of the hydraulic fluid at the cooler
inlet and the cooling water inlet).
4) The reduction in the fluid temperature through the cooler and the temperature in the
reservoir.
P Chapple April 2006.
Tutorial Questions
6