LINKÖPINGS TEKNISKA HÖGSKOLA
IKP
Fluid och Mekanisk Systemteknik
1.
2(6)
EXAMINATION
TMHP 51
2005-12-15
a) Cavitation i hydraulic orifices
The figure shows measured flow versus outlet pressure for an orifice supplied
with constant inlet pressure, pu = 200 bar. Cavitation starts when the outlet
pressure is reduced to pd = 75 bar.
Assume that the inlet pressure to the orifice is changed to pu = 160 bar. At which
level of the outlet pressure pd can now cavitation be expected?
Which highest inlet pressure (pu) can be accepted for cavitation free flow if the
lowest outlet pressure is pd = 2,0 bar.
(4p)
b) Water versus mineral oil as fluid in hydraulic servo systems
In a hydraulic servo system the mineral oil is changed to a mixture of waterglycol. This means that the fluid viscosity is reduced a factor 10 and the effective
bulk modulus increased 1,8 times. Describe qualitatively how the water fluid will
influence the resonance frequency ( h) and damping ( h) in the system.
(2p)
c) Flow forces in a 4-port servo valve
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A 4-port symmetric servo valve is supplied from a constant pressure controlled
pump adjusted for pp = 210 bar. Max pump flow is qpmax = 74 litre/min. Flow
forces versus valve spool displacement (xv) when the load pressure difference is 0
are shown in a diagram.
Calculate the nominal valve flow qvN (total valve pressure diff. pv = 70 bar).
Assume that the pump pressure in the system above increases to pp = 350 bar.
Calculate the new value for max flow forces, Fsmax (qpmax = 74 litre/min).
(4p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IKP
Fluid och Mekanisk Systemteknik
2.
3(6)
EXAMINATION
TMHP 51
2005-12-15
a) Servo valves with different “lapping”
In position servos normally 4-pors symmetric servo valves with null-lapping
(critical center) or under-lapping are used.
Describe qualitatively how the ”lapping” will influence stability and stiffness of
a proportional controlled position servo.
(3p)
b) Direct controlled servo valve
The figure shows a direct controlled servo valve. Compare this valve with a 2stage servo valve (electro-hydraulic pilot stage) according to hysteresis and
bandwidth.
(2p)
c) Valve and pump controlled position servo
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The figure shows schematically a valve controlled (4-port ”critical center” valve)
and a pump controlled position servo. Cylinder and load are identical and both
servos have proportional controllers (Greg = Ksa). The controller gain (Ksa) is
adjusted for the same amplitude margin, Am = 6 dB when the resonance frequency
( h) has its lowest value. The leakage flow coefficients (Kce and Ct) have the same
value as well as the flow gain for valve and pump, Kqi = Kpi (qp =i·Kpi). The servo
valve and the pump controller have equal threshold values, iT = in.
Calculate the position error ratio Xp4-v/ Xpp for the two systems according to
the threshold ( iT).
(5p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IKP
Fluid och Mekanisk Systemteknik
3.
EXAMINATION
TMHP 51
2005-12-15
4(6)
Position servo with valve controlled cylinders
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The figure shows an electro-hydraulic position servo with a 4-port servo valve and
two mechanically connected asymmetric cylinders. The load is a single mass Mt.
The servo has proportional position control with the feedback gain Kf and the
controller gain Ksa. The servo valve is null-lapped and symmetric and its nullcoefficients are Kqi0 and Kc0. The valve bandwidth is high. The supply pressure
ps, is constant. Cylinder piston area is Ap and the total pressurised volume
between valve and pistons is Vt = V1+V2. The cylinders can be assumed as loss
free. The bandwidth of the servo system is b (at the amplitude - 3 dB).
The system has the following parameter values:
Ap = 1,96.10-3 m2
Mt = 800 kg
Vt = 1,0.10-3 m3
ps = 21 MPa
Kf = 25 V/m
a) Kce-value for a bandwidth of
b
= 1200 MPa
Kqi0 = 0,013 m3/As
e
= 25 rad/s
Calculate the required Kce-value so that the closed loop servo can reach a
bandwidth of b = 25 rad/s, with an amplitude margin of Am = 6 dB in the most
critical operation point.
(5p)
b) Feed forward loop to reduce the velocity error
Assume that the piston position (xp) has to follow the command signal, uc =
Ax·sin( t). In order to reduce the velocity error the command signal shall be fed
forward via servo amplifier to the valve to create a signal corresponding to the
required velocity profile for the cylinder pistons.
Show in a block diagram how you will implement the feed forward loop and
calculate the steady state feed forward gain. Assume that Ksa is adjusted for the
bandwidth, b = 25 rad/s.
(5p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IKP
Fluid och Mekanisk Systemteknik
4.
5(6)
EXAMINATION
TMHP 51
2005-12-15
Linear position servo with an inner velocity feedback
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The figure shows an electro-hydraulic linear position servo with a valve controlled cylinder. The controller is proportional, with the gain Ksav. The position
feedback gain is Kf and the velocity feedback gain is Kfv. The servo valve is of 4port type, null-lapped, high bandwidth and the null coefficients are Kqi0 and Kc0.
The cylinder volumes are V1 = V2 = Vt/2 and the bulk modulus is e. The cylinder
piston area is Ap and the cylinder losses are very low. The cylinder is loaded by
the mass Mt and an external force FL.
I service the system has the following parameter values:
Ap = 1,96.10-3 m2
Mt = 900 kg
e = 1000 MPa
-2
.
-3
3
3
Vt = 1,0 10 m
Kqi0 = 1.0 10 m /As
Kc0 = 1,0.10-11 m5/Ns
'
Kf = 20 V/m
Ksav = 0,80 A/V
h = 320 rad/s
a) Hydraulic damping with velocity feedback
For the servo system, including velocity feedback, has the un-damped resonance
frequency been measured to h' = 320 rad/s.
Calculate the hydraulic damping
'
h
at this frequency.
The low hydraulic damping can provide oscillation problems. Describe
qualitatively a method to reduce the oscillation problems.
(5p)
b) Steady state stiffness versus velocity feedback gain
Derive from the block diagram above the steady state stiffness of the closed loop
system,
FL
Xp
as a function of the velocity feedback gain Kvfv and calculate
s
0
the stiffness.
(5p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IKP
Fluid och Mekanisk Systemteknik
5.
6(6)
EXAMINATION
TMHP 51
2005-12-15
Velocity servo with pump controlled motor and two inertia loads
The figure illustrates an electro-hydraulic velocity servo with a pump controlled
motor loaded by two inertias (J1 and J2). The controller is of integrating type with
the gain Ksa. The pump displacement setting controller has the transfer function:
Ki
p
, with the displacement setting coefficient K i = 20 A-1 and the brake
i 1 s
s
frequency s = 100 rad/s. The pump shaft speed is p = 157 rad/s and the
displacement is Dp = 5,6.10-6 m3/rad. The volumes between pump and motor are
V1 = V2 = 0,6 litre and the effective bulk modulus is e = 800 MPa. The motor
displacement is Dm = 19.10-6 m3/rad and the inertias on the motor shaft is J1 = J2
= 0,5 kgm2. The torsion spring constant between the masses is KL = 2000
Nm/rad. The transmission leakage flow coefficient is Ct = 4,0.10-12 m5/Ns and
the viscous friction coefficient is Bm = 0. The low pressure side has constant pm.
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a) Transmission dynamics versus load dynamics
Calculate the transmission hydraulic resonance frequency ( h) and compare
with the load dynamics.
Show schematically in a bode-diagram the amplitude of the loop gain Au(s).
(5p)
b) Acceleration feedback for increased damping
In order to increase the hydraulic damping ( h) an acceleration feedback from the
hydraulic motor shaft shall be implemented.
Show in a block-diagram how you will implement the feedback and show with
equations its influence on the hydraulic damping.
Is the bandwidth of the pump controller ( s) high enough to not influence the
damping?
(5p)
LINKÖPINGS UNIVERSITET
Department of Mechanical Engineering
Fluid and Mechanical Engineering Systems
1(5)
SOLUTIONS FOR EXAMINATION
TMHP 51
2005-12-15
SOLUTIONS FOR EXAMINATION, TMHP51
1.
a) Cavitation in hydraulic orifices
pu = 200 bar and pd = 75 bar gives cavitation.
The diagram gives C2
pdcav
pu
1
pu = 160 bar in eq. (1)
pdcav
0,625
0,375 pu (1).
pdcav = 60 bar.
Cavitation free flow and pd = 2 bar
pumax = pd/0,375 = 5,3 bar.
(4p)
b) Water versus mineral oil as fluid in hydraulic servo systems
The resonance frequency and damping for an actuator with one control volume and load
e
is given by the equations.
h
Ap2
Vp M t
,
K ce
2 Ap
h
Mt
. The high bulk modulus of
Vp
e
water increases both the resonance frequency and damping. Low viscosity increases
the leakage flow and the Kce-value, which increases the damping.
(2p)
c) Flow forces in a 4-port servo valve
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Pump pressure, pp = 210 bar, max pump flow, qpmax = 74 litre/min and pL = 0.
Steady state flow forces: Fs
valve flow as qv
Cq w xv
Nominal valve flow: qv
2C q w xv
pp
pv cos . pv = pp and pL = 0 gives the
(1). Finally Fs max
Cq w xv
pp
qvN
qvmax = qpmax and increased pp to 350 bar in eq. (2)
qp
2
cos
x v max
xv
Fs max
qv max p p (2).
pvN
= 61 litre/min.
pp
85
350
= 110 N
210
(4p)
LINKÖPINGS UNIVERSITET
Department of Mechanical Engineering
Fluid and Mechanical Engineering Systems
2.
2(5)
SOLUTIONS FOR EXAMINATION
TMHP 51
2005-12-15
a) Servo valves with different “lapping”
Null-lapping gives a linear flow gain and low leakage around “zero”, which will
improve the stiffness but low hydraulic damping will reduce the stability margin.
Under-lapping gives high flow gain and high hydraulic damping around “zero”
operation. This will improve the stability but reduce the stiffness.
(3p)
b) Direct controlled servo valve
In comparison with a 2-stage valve the direct controlled valve has low control forces on
the main spool. Low control forces give high hysteresis because of friction and flow
forces in the valve and the bandwidth will be low because of low acceleration of the
main spool.
(2p)
c) Valve and pump controlled position servo
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Calculate the position error ratio Xp4-v/ Xpp for the two systems according to the
threshold ( iT) when the systems have equal parameters and designed for Am = 6 dB in
the most critical operation point. Kce = Ct and Kqi = Kpi.
Position error from threshold:
Am = 6 dB
Steady state loop gain: Kv =
Valve control:
Kv 4 v
Kv p
X p K f K sa
h
h 4 v
K sa K qi K f / Ap
K sa K pi K f / Ap
2 K ce
4
e
Vt
h· h
. Pump control:
K sa 4 v
K sap
iT
K f K sa
Xp
iT
4.
X p4
X pp
v
h
h p
K sap
K sa 4
v
1
Ct e
2 Vt
1
= 0,25
4
(5p)
LINKÖPINGS UNIVERSITET
Department of Mechanical Engineering
Fluid and Mechanical Engineering Systems
3.
3(5)
SOLUTIONS FOR EXAMINATION
TMHP 51
2005-12-15
Position servo with valve controlled cylinders
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Ap = 1,96.10-3 m2
ps = 21 MPa
Mt = 800 kg
Kqi0 = 0,013 m3/As
a) Kce-value for a bandwidth of
b
= 25 rad/s
Steady state loop gain Kv =
Am = 6 dB
Valve controlled cylinder:
the bandwidth:
b
h
4
h
Ap2
Vt M t
2 K ce
h
e
Vt = 1,0.10-3 m3
= 1200 MPa
Kf = 25 V/m
e
e
h· h
,
K ce
Ap
bVt
h
K ce
Vt
and bandwidth
2
b
= Kv = 25 1/s .
Mt
, which gives
Vt
e
= 1,04·10-11 m5/Ns
e
(5p)
b) Feed forward loop to reduce the velocity error
Block diagram showing the implementation of the feed forward loop.
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The feed forward block includes a derivation (s) of the position command signal (uc =
Ax·sin( t), which means that the feed forward signal represents a velocity signal. The
K qi
block diagram shows that the gain from command signal to piston velocity is: K sa
.
Ap
If the steady state feed forward gain is set to K ff
Ap
K sa K qi
it represents a true velocity
signal in the system.
Calculation of Kff:
K sa
K qi
Ap
b
Kv
K sa
K qi
Ap
K f . Kv = 25 1/s and Kf = 25 V/m gives
= 1,0, which gives the steady state feed forward gain Kff = 1,0.
(5p)
LINKÖPINGS UNIVERSITET
Department of Mechanical Engineering
Fluid and Mechanical Engineering Systems
4.
4(5)
SOLUTIONS FOR EXAMINATION
TMHP 51
2005-12-15
Linear position servo with velocity feedback
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Parameter values:
Ap = 1,96.10-3 m2
Vt = 1,0.10-3 m3
Kf = 20 V/m
Mt = 900 kg
Kqi0 = 1.0 10-2 m3/As
Ksav = 0,80 A/V
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= 1000 MPa
Kc0 = 1,0.10-11 m5/Ns
'
h = 320 rad/s
e
a) Hydraulic damping with velocity feedback
With velocity feedback the un-damped resonance frequency is
4
The basic resonance frequency ( h) is:
'
h
above gives
K vfv and
h
'
h
h
h
e
Ap2
Vt M t
'
h
= 320 rad/s.
= 131 rad/s. The block diagram
/ K vfv . K vfv
'
h
2
Kvfv = 6,0 and finally
h
'
h
K co
Ap
Mt
Vt
e
1
= 0,0625.
K vfv
A negative dynamic load pressure feedback or acceleration feedback can be used to
increase the low hydraulic damping without any influence on the steady state stiffness.
(5p)
b) Steady state stiffness versus velocity feedback gain
From the block diagram above the closed loop stiffness can be derived as:
K
2 h
s2
s 1 K vfv s K f K sav qi
2
K vfv h K vfv h
Ap
FL
. The steady state part is
Sc
Xp
K ce
Vt
1
s
4 e K ce
Ap2
FL
Xp
FL
Xp
s
0
K vfv K sav K qi K f
Ap2
Ap K vfv
K ce
K sav K qi 0 K f Ap
s
0
Kc0
. Numerically the steady state stiffness is:
= 3,14·107 N/m.
(5p)
LINKÖPINGS UNIVERSITET
Department of Mechanical Engineering
Fluid and Mechanical Engineering Systems
5.
5(5)
SOLUTIONS FOR EXAMINATION
TMHP 51
2005-12-15
Velocity servo with pump controlled motor and two inertia loads
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= 157 rad/s, Dp = 5,6.10-6 m3/rad, V1 = V2 = 0,6 litre, e = 800 MPa, Dm = 19.10-6
m3/rad, J1 = J2 = 0,5 kgm2, KL = 2000 Nm/rad and Ct = 4,0.10-12 m5/Ns.
p
a) Transmission dynamics versus load dynamics
The hydraulic frequency for the transmission is
Dm2
. Numerically:
Vt J 1 J 2
e
h
2
800 106 19 10 6
= 22 rad/s. The load dynamics include two frequencies,
0,6 10 3 0,5 0,5
h
and
1.
The lowest one is
KL
.
J2
a
2000
= 63 rad/s.
0,5
a
h
is dominant.
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(5p)
b) Acceleration feedback for increased damping
Implementation of acceleration feedback.
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Influence on hydraulic damping Gh ( s )
1
s
2
2
2
h
'
h
h
h
2
K ac
Ki
1
Dm 1 s /
p
h
h
K ac
Ki
1
Dm 1 s /
p
Dp s 1
s
Dp
s
Since s = 100 rad/s, is higher than both
damping is marginal.
h
and
a
its influence on the hydraulic
(5p)
a