aerospace applications of pkm prof. rosario sinatra dipartimento di ingegneria industriale e...
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Aerospace applications of PKM
Prof. Rosario Sinatra
Dipartimento di Ingegneria Industriale e MeccanicaUniversità degli Studi di Catania
March 30, 2007
EURON07 WINTER SCHOOL PARALLEL ROBOTS: Theory and Applications 2nd International UMH Robotics Winter School Flamingo Oasis Hotel, Benidorm, SpainMarch 26 - 30, 2007
AEROSPACE MECHANISMSPOINTING SYSTEMS FOR SATELLITE ANTENNAS
CONTROL SYSTEM SCHEME FOR POINTING ERROR COMPENSATION
RESEARCH PROJECTS IN WITH PARTNERSHIP WITH
THE SATELLITE COMMUNICATIONS REQUIRES A VERY
ACCURATE POINTING SYSTEM, COMPOSED BY
DIFFERENT ELECTRO-MECHANICAL DEVICES
Sinatra Rosario
Pirrotta Simone
ANTENNA MECHANICAL and MECHANISM DESIGN SECTION, ING. ABERTO MESCHINI
AEROSPACE MECHANISMSPOINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA
PARABOLIC REFLECTOR
SUBREFLECTOR
FEED
OLD PONTING CONCEPT NEW PONTING CONCEPT
W24
AEROSPACE MECHANISMS
RADIATION DIAGRAM
ORBITAL RE-POINTING
RE-POINTING BY SUBREFLECTOR DYNAMIC POSITIONING
POINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA
AEROSPACE MECHANISMS
FIXED PLATFORM
MOBILE PLATFORM
LEGS
)(11 SiiiiPSP
OCQCOOOOOp KINEMATIC EQUATION
SPHERICAL JOINT
PRISMATIC JOINT
UNIVERSAL JOINT
POINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA
tJtJq
tJq
uQrpuQrp
][][q i
Tiii i
''
AEROSPACE MECHANISMS
0 500 1000 1500 2000 2500 3000 3500 4000-1
0
1
L1
Elongazioni dei giunti attuati
0 500 1000 1500 2000 2500 3000 3500 4000-5
0
5
L2
0 500 1000 1500 2000 2500 3000 3500 4000-1
0
1
L3
0 500 1000 1500 2000 2500 3000 3500 4000-2
0
2
L4
0 500 1000 1500 2000 2500 3000 3500 4000-1
0
1
L5
0 500 1000 1500 2000 2500 3000 3500 4000-0.5
0
0.5
L6
t (secondi)
0 500 1000 1500 2000 2500 3000 3500 4000-5
0
5x 10
-3
L1
Velocità dei giunti attuati
0 500 1000 1500 2000 2500 3000 3500 4000-0.02
0
0.02
L2
0 500 1000 1500 2000 2500 3000 3500 4000-0.01
0
0.01
L3
0 500 1000 1500 2000 2500 3000 3500 4000-0.01
0
0.01
L4
0 500 1000 1500 2000 2500 3000 3500 4000-5
0
5x 10
-3
L5
0 500 1000 1500 2000 2500 3000 3500 4000-2
0
2x 10
-3
L6
t (secondi)
0 500 1000 1500 2000 2500 3000 3500 4000-8
0
8x 10
-5
L1
Accelerazioni dei giunti attuati
0 500 1000 1500 2000 2500 3000 3500 4000-2
0
2x 10
-4
L2
0 500 1000 1500 2000 2500 3000 3500 4000-1
0
1x 10
-4
L3
0 500 1000 1500 2000 2500 3000 3500 4000-1
0
1x 10
-4
L4
0 500 1000 1500 2000 2500 3000 3500 4000-8
0
8x 10
-5
L5
0 500 1000 1500 2000 2500 3000 3500 4000-3
0
3x 10
-5
L6
t (secondi)
DISPLACEMENT VELOCITY ACCELERATION
0 500 1000 1500 2000 2500 3000 3500 4000-0.02
0
0.02
0.04
0.06
0.08
0.1
gra
di
t (secondi)
Disturbo totale in normal mode
-0.4
-0.3
-0.2
-0.1
0
0.1
-80.7-80.6
-80.5-80.4
-80.3-80.2
476.2
476.3
476.4
476.5
476.6
476.7
asse X (mm)
Traiettoria del centro del subriflettore
asse Y (mm)
asse
Z
(m
m)
ORBITAL DISTURBANCE
SIGNAL (STATION KEEPING)
SUBREFLECTOR’S CENTRE 3D-PATH
KINEMATICS VARIABLES OF
THE ACTUATED PRISMATIC
JOINTS
POINTING SYSTEM FOR DOUBLE REFLECTOR ANTENNA
AEROSPACE MECHANISMS2 DOF POINTING SYSTEM
FIXED PLATFORM
MOBILE PLATFORM
LINEAR ACTUATOR
0
coscos2
sincossin
cossinsin2sinsincoscos2
sincossin2coscos22
0
coscos2
sincossin
cossinsin2sinsincoscos2
sincossin2coscos22
20
20
22100
10120
210202121
2
1122100222
20
20
22100
10120
210202121
2
1122100121
ABBA
AA
BB
BA
ABBA
AA
BB
BA
zzlzz
zz
zzbb
bzzss
zzlzz
zz
zzbb
bzzss
POINTING CONTROL RELATIONS
AEROSPACE MECHANISMS
MATLAB GUI FOR DIRECT AND INVERSE KINEMATICS
z = -1.6529E -5+ 0.135*x -0.135*y -3.8847E -6*x *x + 8.9256E -8*x *y + 4.0004E -6*y *y
MATLAB GRAPHICS OUTPUT
[deg]
3213.6101986.1
6367.2101091.8
103511.1
42
41
91
322
31
8
12
222
173
23
18
211
1
ssssss
ssssss
ss
[deg]
0384.1
8832.1102428.1
100636.1103511.1
42
41
8
12
222
173
23
17
22
21
521
1
2
ss
ssssss
ssss
POINTING SURFACE
1 = f(s1, s2)
2 DOF POINTING SYSTEM
AEROSPACE MECHANISMS
RESIDUALS MAP AND
DISTRIBUTION WITH RESPETC TO ANALYTIC
POINTING RELATIONS
2 DOF POINTING SYSTEM
-0.004
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0.004
0.005
-30 -20 -10 0 10 20 30
Elongazione s1 [mm]
( 1
s- 1
CA
D)
[deg
]s2=-25 [mm] s2=-20[mm] s2=-15 [mm]
s2=-10[mm] s2=-5 [mm] s2=0 [mm]
s2=5 [mm] s2=10[mm] s2=15 [mm]
s2=20[mm] s2=25 [mm]
COMPARISON WITH CAD “EUCLID”
KINEMATIC RESULTS
0
5
10
15
20
25
30
35
40
45
-0.000179 -0.000124 -0.000068 -0.000012 0.000044 0.000100Residuo su 1 [deg]
Fre
que
nza
perc
entu
ale
[%] Media Dev. st.
-4.3360E-06 8.9632E-05[deg] [deg]
AEROSPACE MECHANISMSULTRASONIC MOTOR
2 Supply Channels
ELECTRICAL
Equal amplitude VmaxA=VmaxB
Opposite phase (90°)
Flexural vibration
2 waves with time phase
of 90°
Rotational motion around
vertical axes
ROTORS
STATOR
Travelling wave
PIEZOELECTRICS
ROTORS
STATOR
AEROSPACE MECHANISMSULTRASONIC MOTOR
NORMAL AND TANGENTIAL FORCES
FROM ROTOR TO STATOR
PRELOAD FORCE
EXTERNAL TORQUE
NORMAL AND TANGENTIAL FORCES
FROM STATOR TO ROTOR
MULTIBODY SYSTEM
AEROSPACE MECHANISMSULTRASONIC MOTOR
EQUATIONS OF MOTION
),,,(),( ppFpFvΘpKpCpM fTfNstatstatstat ww
appffzfr FwFwCwM ),(int p
appfr wCI ),,,(int pp
appint
appint
TN
r
rn,4
n,n21n,n
f
f
r
z
rn2,4
4,n211n,nn,n
f
f
FF
FFv
M
10
00
0I
100
0
0M
0
w
w
p
p
I
C000
1000
00I
C0
0010
0
0CMKM
I0
w
w
p
p
Piezo elements' thickness - tp Stator thickness - ts
Inte
rfac
e th
ickn
ess
- ti
Too
th h
eigh
t - h
t
Piezo elements' inner radius - rpi
Piezo elements' outer radius - rpe
Stator's inner radius - rsi
Teeth inner radius - rti
Teeth outer radius - rte
Stator's outer radius - rse
AEROSPACE MECHANISMSULTRASONIC MOTOR
a)
b)
Dv>0
V rot
V stat
x l-x l x r-x r x
z T res
T m ot +
T m ot + T m ot -
T res
V rot
V stat
Dv = 0Dv>0
Dv<0
x lx r-x l -x r x
z
)22(2
)(2)(220
motmott
ttmdrtapp
TTNr
drpdrphtNrl
r
r
)2(2)(220
motttmdrtapp TNrdrphtNr
l
)2(2)(220
mottw
mdrT NdrphtNl
TΦ
F
drptN twrN
l
0)(22 ΦF
)22(2
)(2
)(22
0
motmot
tw
tw
mdrT
N
drp
drphtN
l
r
r
TT
Φ
Φ
F
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25-0.5
0
0.5
1
1.5
2
2.5
3x 10
5
Pressure [N/m2]
Contact angle l [rad]
Hertz
Linear stiffness
Visco-elastic contact
Hertz second formulation
r
Eapp
r
tEapp
tt
ll
AtN
CF
AtN
rCF
rr
x33
2 28,0
2
2
6,1
TORQUE CALCULATION
AREA-FORCE RELATIONSHIP
AEROSPACE MECHANISMSULTRASONIC MOTOR
LOAD PULLEY
ULTRASONIC MOTOR
TACHOMETER
WEIGHT
Torque-speed curve (F app =39.8N, V max =300V, N =7, d =0.23, h =0.08)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Angular speed [rad/s]
Tor
que
[Nm
]
Experimental
Symulated
Torque-speed curves (Vmax =300 V, d =0.07, h =0.05)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Speed [rad/s]
To
rqu
e
[Nm
]
Prec=1 NPrec=5 NPrec=10 NPrec=15 NPrec=20 NPrec=25 NPrec=30 NPrec=38 NPrec=45 NPrec=60 NPrec=80 NPrec=100 NPrec=130 N
AEROSPACE MECHANISMSULTRASONIC MOTOR
Torque-speed curves (Prec =10 N, d =0.07, h =0.05)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Speed [rad/s]
To
rqu
e [
Nm
]
Vmax=100 V
Vmax=150 V
Vmax=200 V
Vmax=250 V
Vmax=300 V
Vmax=350V
Torque-speed curves (Prec =40 N, d =0.07, h =0.05)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.5 1 1.5 2 2.5
Speed [rad/s]
To
rqu
e [
Nm
]
Vmax=100 V
Vmax=150 V
Vmax=200 V
Vmax=250 V
Vmax=300 V
Vmax=350V
Torque-speed curves (Prec =15 N, Vmax =300 V, h =0.05)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Speed [rad/s]
To
rqu
e [
Nm
]
11111
TORQUE-SPEED CURVES PARAMETRIZED WITH RESPECT TO:
1-MAXIMUM VOLTAGE AMPLITUDE (CASE a and b)
2-FRICTION COEFFICIENT
A. Meschini, R. Sinatra and S. Pirrotta, 2002. A Parallel Mechanism for a Gregorian offset Satellitare Antenna with double reflector, Proceedings of the WORKSHOP on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, October 3–4, Quebec City, Quebec.
A. Cammarata and R. Sinatra, 2005, Dynamics of a two-dof parallel pointing mechanism, Fifth ASME International Conference on Multibody Systems, Nonlinear Dynamics and Control , Sept. 24-28, 2005, Long Beach, California, USA. R. Di Gregorio, A. Cammarata and R. Sinatra, 2005, On The Dynamic Isotropy Of 2-Dof Mechanisms, Fifth ASME International Conference on Multibody Systems, Nonlinear Dynamics and Control , Sept. 24-28, 2005, Long Beach, California, USA.
R. Sinatra, D. Scalora and A. Meschini, 2004, Direct Kinematics of a Parallel Pointing Mechanism Configuration, Proceedings of the WSEAS Conferences, August 17-19, 2004, Corfu, Greece.
S. Pirrotta, R. Sinatra, A. Meschini, 2006. Evaluation of the Effect of Preaload Force on Resonance Frequencies for a Traveling Wave Ultrasonic Motor, IEEE Transactions on ultrasonics, ferroelectrics, and frequency control, Vol. 53, n.4, pp. 746-753.
S. Pirrotta, R. Sinatra and A. Meschini, 2007. A novel simulation model for ring type ultrasonic motor, Meccanica International Journal, Vol. 42, n.2, pp. 127-139.
References