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LINKÖPINGS TEKNISKA HÖGSKOLA
IEI
Fluid and Mechanical Engineering Systems
1.
2(6)
EXAMINATION
TMHP 51
2008-08-16
a) Cavitation in orifices
In hydraulic systems cavitation occur downstream orifices with high pressure
drops. For an orifice with a constant inlet pressure of p1 = 200 bar cavitation will
start when the outlet pressure is reduced to p2 = 72 bar. Assume that the inlet
pressure is changed to p1 = 280 bar.
For which value of p2 can cavitation now be expected?
A way to avoid cavitation is to split the pressure drop over two or more orifices in
serial connection. Describe with equations, which of two serial connected orifices
can take the highest pressure drop without any risk for cavitation. (Assume that the
outlet pressure for the second orifice is zero).
(4p)
b) Servo valve with bushing
The main stage in an advanced servo valve consists of a spool and a valve
bushing. Describe qualitatively the benefits of using a bushing compared to a
valve without bushing it the pressure level is high.
(3p)
c) Flow forces on a spool valve in constant pressure system
The figure below shows a 4-port critical centre servo valve connected to a constant
pressure controlled pump. A diagram shows the measured flow forces versus valve
displacement, xv.
pp
qp
Dpv
xv
qv
Fs
65 N
np
pT = 0
Fs
xv
0
0,6*xvmax
xvmax
Assume that the max pump flow (qpmax) is increased to the same level as the max
flow capacity of the valve with the same pressure drop, Δpv as for the measured
case. Show in a diagram and calculate the maximum flow forces for that case.
(3p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IEI
Fluid and Mechanical Engineering Systems
2.
3(6)
EXAMINATION
TMHP 51
2008-08-16
a) Valve wear and its influence on valve coefficients
Wear on the orifice edges in a zero-lapped servo valve will cause changes in the
steady state characteristics around neutral spool position (xv = 0). Which of the
valve coefficients will be most affected by wear and how is the closed loop
stiffness in a position servo with proportional controller gain influenced by this?
(3p)
b) Direct driven servo valve in a position servo
A direct driven valve, according to the figure below, is used in a position servo
with a proportional controller. Describe qualitatively how the flow forces will
influence the stability of the servo system.
A
B
P
T
Proportionalmagnet
(2p)
c) Valve controlled and pump controlled position servo
The figure below shows a valve controlled and a pump controlled motor. Both
systems are used as rotating position servos with proportional control. Volumes,
bulk modulus, motor displacement and load inertia are equal in both systems.
Assume that in the most critical operating point both systems have the same
flow/pressure-coefficient (Kce = Ct) and the same amplitude margin, Am = 6 dB.
Show with equation which of the system as will given the highest steady state
stiffness, |-ΔTL/Δθm|s→0. (The stiffness of the closed loop system is asked for).
Uc
+
Kf
Uc
V1
ep
+
Dm
qm
V2
Kf
-
Jt
TL
wp
p1 V 1
Dm
Dp
pm =
konst
qm
Jt
TL
p2 V 2
(5p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IEI
Fluid and Mechanical Engineering Systems
3.
EXAMINATION
TMHP 51
2008-08-16
4(6)
Position servo with 3-port servo valve and an asymmetric cylinder
The figure shows an electro-hydraulic position servo with a 3-port valve and an
asymmetric cylinder loaded by a mass and an external force. The servo has
proportional position control with a feedback gain of Kfx and a controller gain of
Kreg. The servo valve is zero-lapped and it has symmetric and matched orifices
and the null-coefficients are Kqi0 and Kc0. The valve has a high bandwidth but has
a threshold, iT. The supply pressure, ps is constant. The piston area is A1, the area
on the piston rod side is A1/2 and the cylinder volume on the piston side is V1. The
cylinder is assumed to have no leakage and friction. The bandwidth of the closed
loop servo system is ωb (with the amplitude –3 dB, for a given operation point).
Parameter values:
A1 = 1,96.10-3 m2
V1 = 0,25.10-3 m3
Kc0 = 8,0.10-12 m5/Ns
iT = 0,4 mA
Mt = 200 kg
ps = 14 MPa
Kfx = 25 V/m
βe = 1200 MPa
Kqi0 = 0,013 m3/As
ωb = 15 rad/s
a) Steady state position error
Calculate the maximum position error (ΔXp) which can be caused by a load
disturbance ΔFL = 1000 N and together with the threshold of the valve, iT.
(5p)
b) Lag-compensation of the control loop
Assume that the proportional position controller (Kreg) is extended by a lag filter
1 + s / ω LC
. The steady state gain α = 2,0.
with the transfer function G LC ( s ) = α
1 + s ⋅ α / ω LC
Calculate for this case the position error caused by a load disturbance only,
(according to task a).
(3p)
c) Influence from a servo valve with slow response
Discuss in general how the bandwidth of the servo system will be influenced if
the valve response is slower that the dynamics of the actuator and load.
(2p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IEI
Fluid and Mechanical Engineering Systems
4.
5(6)
EXAMINATION
TMHP 51
2008-08-16
Angular position servo with dynamic pressure feedback
Kf
Uc
+
+
Gp(s)
Greg
V1
ps
qm
Jt
pL
TL
V2
The figure shows an elektro-hydraulic position servo with a valve controlled
motor. The proportional controller has the gain Greg = Ksa = 0,04 A/V. In order to
increase the hydraulic damping a dynamic load pressure feedback with the gain
function Gp(s)= Kpf.s/(1 + s/ωf) is implemented. The servo valve is of 4-port type,
zero-lapped, with high bandwidth and its zero-coefficients are Kqi0 = 0,013 m3/As
and Kc0 = 1,0.10-12 m5/Ns. The volumes between valve and motor are V1 = V2 =
0,5 litre and its bulk modulus is β e = 1000 MPa. The motor displacement is Dm =
6,4.10-6 m3/rad, the leakage flow coefficient is Ctm = 8,0.10-13 m5/Ns and the
viscous friction coefficient Bm = 0. The motor shaft inertia is Jt = 0,5 kgm2.
a) Adjustment of the pressure feedback for a given hydraulic damping
Calculate the static gain Kpf for the load pressure feedback, which gives the
hydraulic damping δh = 0,35 at the frequency ωh. The break frequency in the
pressure feedback filter is ωf = ωh/2.
(7p)
b) The pressure feedback and its influence on steady state stiffness
Show with equations that the dynamic pressure feedback has a marginal effect on
the steady state stiffness of the closed loop system.
(3p)
LINKÖPINGS TEKNISKA HÖGSKOLA
IEI
Fluid and Mechanical Engineering Systems
5.
6(6)
EXAMINATION
TMHP 51
2008-08-16
Load dynamics for a valve controlled hydraulic cylinder
The figure below shows a valve controlled hydraulic cylinder loaded by the
masses M1 and M2. The connection between the masses includes a spring and a
damper (spring constant KL and viscous friction coeff BL). The piston position xp
is fed back to a proportional regulator with the gain Greg = Ksa.
xp
KL
Ap
p1 C1
Ap
M2
M1
C2 p2
Position
transducer
uc +
uf -
Servo
amplifier
Ksa
BL
xL
Kf
i
Au(s)
Ps = const.
The block diagram from valve input signal (i) to piston velocity (sXp) is:
Kqi
i ___
Ap +
-
Ap
__________
Vt
Kce + ___ s
4be
PL
Ap
sXp
1
__________
GLX(s)
(M1 + M2) s
s2
+
2δ a
s +1
ωa
The transfer function of the mechanics is G LX ( s ) =
, (ωa < ω1)
2δ 1
s
+
s +1
ω12 ω1
ω
2
a
2
a) Block diagram, frequency and damping of the position servo
Reduce the feedback in the above block diagram and draw a new one for the
complete position servo. Define the hydraulic resonance frequency and the
damping (ωh, δh).
(5p)
b) Position servo loop gain for Kh << KL
Derive from the block diagram an expression of the position servo loop gain Au(s)
when the hydraulic spring constant Kh = 4β eAp2/Vt is much lower than the
mechanical spring constant KL (ωh << ωa).
(5p)