Multibody dynamics discipline, and dynamic simulation in control structure interaction (CSI) design are discussed. The use, capabilities, and architecture of the Large Angle Transient Dynamics (LATDYN) code as a simulation tool are explained. A generic joint body with various types of hinge connections; finite element and element coordinate systems; results of a flexible beam spin-up on a plane; mini-mast deployment; space crane and robotic slewing manipulations; a potential CSI test article; and multibody benchmark experiments are also described

Chang, C. W.

Housner, J. M.

Wu, S. C.

English

NASA Technical Reports Server

N90-21068
CONTROLLED MULTIBODY DYNAMICS SIMULATION
FOR
LARGE SPACE STRUCTURES
J. M. Housner
NASA Langley Research Center
Hampton, Virginia
S. C. Wu and C. W. Chang
The Comtek Company
Yorktown, Virginia
Third Annual CSI Conference
San Diego, California
January 30 - February 2, 1989
91
https://ntrs.nasa.gov/search.jsp?R=19900011752 2020-03-19T22:48:18+00:00Z
MULTIBODYDYNAMICSDISCIPLINE
The multibody dynamics discipline involves the large relative
motions of connected flexible bodies. Thus, the configuration of
the multibody system is time-varying, generally resulting in time-
varying inertial properties and sometimes in time-varying
stiffness properties. Hinge connections between the bodies are
necessary to enable the changing relative orientations. Because
there are multiple bodies, it is quite likely there will also be
multiple control systems with multiple objectives. Multibody
dynamics finds application in various fields. Many applications
impose constraints on the multibody system and the handling of
these is a critical aspect of the discipline.
o DEFINITION: Interconnected Flexible Body Dynamics With
Time Varying Relative Orientations
- Time Varying Stiffness and Mass
- Hinge Connections of Various Types
- Multiple Control Systems
o APPLICATIONS:
- Mechanisms
- Unfolding Deployment/Retraction
- Articulation
o CONSTRAINTS
- Motion Limiters, Mechanical Regulators
- Connect/Disconnect
- Lock/Unlock
- Robotic Hand-Off
92
THE ROLE OF MULTIBODY DYNAMICS SIMULATION ANALYSIS IN CSI DESIGN
Four roles are here identified for multibody dynamics
simulation. Use of this simulation early in the design process can
be most effective as it can reveal design shortcomings before
commitment to a design concept. Multibody simulation can be used
to address performance degradation, constraint violation and
stability. Invariably the simulation models are more refined then
the design models and can thus be used to judge the suitability of
the design models. The simulation models usually incorporate
modes left out of the design models, thus addressing "spillover",
uncertainties in structure, controller, sensors and actuators, and
nonlinearities which are often neglected in design.
o IDENTIFIES TECHNICAL ISSUES EARLY IN DESIGN PROCESS
LESS EXPENSIVE THAN EXPERIMENTATION
CAPABLE OF PARAMETER STUDIES WITH REFINED MODELS
o ESTABLISHES CONTROLLER PERFORMANCE DEGRADATION
MODAL TRUNCATION, UNCERTAINTIES AND NONLINEARITIES
o ESTABLISHES VIOLATION OF CSI DESIGN CONSTRAINTS
STRUCTURAL MEMBER BUCKLING
ACTUATOR OUTPUT EXCEEDANCE
o EXAMINES STABILITY OF DESIGNED SYSTEM
ACTUATOR AND SENSOR PLACEMENT
LINEAR DESIGN ASSUMPTIONS
93
LATDYN CAPABILITIES
The LATDYN (Large Angle Transient DYNamics) code is a
simulation tool for controlled multibody dynamics. The code is
finite element based with the present version having a limited
element library consisting of mass, spring, damper and beam
elements. The user models each body with finite elements, rather
than with truncated modes or other function sets which have to be
generated outside the multibody program.
Control laws are input through a FORTRAN-based command
language which gives the user internal access to the code from an
external position. Further details on the program architecture are
given in the chart on LATDYN architecture.
Practicalities of control implementation can also be modeled
such as actuators, friction and time delay in digital control.
Two and three dimensional versions are available and results from
these are presented herein. Additional information on the code is
available in references 1 - 3. -- •
An,onn. On-or +,cons,r.o,+on
Space Station robotics
i
i
i
|
94
- i-A.- -: _.
LATDYN CAPABILITIES
o SIMULATION ANALYSIS TOOL FOR LARGE MOTIONS AND DEFORMATIONS
OF CONTROLLED MULTIBODY STRUCTURES FOR,
ASSEMBLY DYNAMICS, ARTICULATING COMPONENTS, ROBOTIC
OPERATIONS
o FINITE ELEMENT BASED STRUCTURAL MODELING
RIGID OR FLEXIBLE COMPONENTS
ARBITRARY GEOMETRY
o EXTENSIVE CONTROLS MODELING
FORTRAN BASED COMMAND LANGUAGE PERMITS SIMPLIFIED USER
INPUT OF CONTROL ALGORITHMS
o ACTUATOR ANq) MOTOR MODELING
FRICTION AND TIME DELAY
o 2-D VERSION DEVELOPED IN 1986
o 3-D WORKING VERSION OPERATIONAL
95
LATDYN ARCHITECTURE
For the structural part of the modeling, user commands
resembling that of a typical general purpose finite element
program are employed. However, for controls, the commands take on
a somewhat different character. The user writes the control law
equations in FORTRAN within a command statement using a defined
protocol to access utilities residing in the LATDYN pre-processor.
(Since most users are well acquainted with FORTRAN this is a
natural language to use.) The pre-processor generates complete
FORTRAN code which is then placed in empty subroutine shells.
This resembles the user-written subroutines employed by other
programs, but has the distinct advantage of relieving the user of
the burden of understanding the complex operations of the code.
The user need not be concerned with what subroutines are created,
nor how data are transferred within the code. This and many other
functions are performed automatically. Finally the generated code
is compiled and linked to the LATDYN computational core.
Furthermore, the user can create his own variables and can
readily specify logic conditions under which commands are to be
activated Or deactivated. This is an important aspect for control
actuators which are only activated once prescribed conditions are
exceeded or can become saturated as in the case of momentum
exchange devices.
FORTRAN
\ / W_ Compiler and
, 0 © "
SUBROUTINE
S J LA  0c L
UTI'I,IES/
I LATDYNPreprocessor
USERS
v
96
GENERIC JOINT BODY WITH VARIOUS TYPES OF HINGE CONNECTIONS
The class of structures to be treated by this program is
joint dominated. That is, the mass of the interconnecting joints
between the bodies represents a significant portion of the total
mass and the orientation of the joint's hinge lines plays an
important role in determining structural behavior. It is thus
reasonable to construct the finite element program with the joints
as a part of the element connectivity. This avoids numerical
problems which can arise due to what might be called "the tail
waging the dog" phenomenon. Furthermore, since large angular
rotations are not vectors, connectivity relationships could be
time varying and quite complex. The use of hinge bodies
circumvents these connectivity complications.
A generic hinge body with several members connected to it
through various types of joints is depicted in the figure.
Accommodations for hinge connections to various members connected
to the hinge body are built into the formulation.
A Cartesian coordinate system is used to measure three
translations of a designated point on a hinge body and a
transformation matrix provides the orientation of three orthogonal
axes embedded into the hinge body. Members are assumed to be hinge-
connected to a hinge body. The connecting hinge line is embedded
into the hinge body and is related to the hinge body axes through
a fixed transformation matrix F. The rotation O about the hinge
line is time varying.
Joint body coordinates _ ._._._evolute connection
Joint body
I Ball
c_
/
/
97
DEFORMED FINITE-ELEMENT AND ELEMENT COORDINATE SYSTEMS
Each structural member is divided into finite elements. A
typical deformed elemen£ is shown in the figure. The orientation
of the element at its ends is monitored by means of a two-element
coordinate system, one at each end. These coordinates move with
the element. The x-axis of the element system is tangent to the
element at its end and the other two orthogona! axe s are parallel
to the principle axes of-the element cross section. The
orientation along the length is found from anassumed polynomial
shape function as in any finite-element analysis.
A convected coordinate system is used to define a reference
for measuring element flexural def0rmations, This separates rigid
body and deformable motion. As shown in the figure _ the convected
x-axis connects the end points of element. Its other two
orthogonal axes roll with the element.
Convected axis End 2
Element coordinates move
with cross section
/ End 1
Deformations are measured from convected axes
98
=
COMPARISON OF RESULTS FOR FLEXIBLE BEAM SPIN-UP ON A PLANE
A flexible rotating beam, with a one hertz fundamental
frequency is accelerated to a constant angular velocity in six
seconds. The results of the LATDYN program are compared with those
from a commercial code known as DADS. (See reference 4 for
further details on this code.) Results are in excellent agreement
with only a slight deviation during the transient region. The
LATDYN model uses two finite elements, but one would have
sufficed. The DADS result can be found in reference 5.
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. / PRESENT ANALYSIS
-o.o, ' I I I i I I I J I , I , I , ] J ] J
O, I, 2, 3. 4. 5, 6. 7, 8. 9.
Time/Fundamental Period
10.
99
MINI-MAST DEPLOYMENT
The Mini-Mast is a 20 meter long, triangular cross-section,
three longeron truss. The truss members are of graphite-epoxy and
the joints, which contain the hinges between the members, are
titanium. Reference 6 provides further details on the truss
properties. The Mini-Mast derives its name from the longer 60
meter mast formerly planned as an on-orbit experiment deployed
from the Space Shuttle's cargo bay. The Mini-Mast was designed
and fabricated by the ASTRO Corporation.
The upper portion of the chart shows a single bay of the
truss. Deployment proceeds by rotating the upper triangle I00
degrees counterclockwise about the vertical axis till the
longerons are in a vertical orientation. Though not shown in the
figure, a diag0nal exists on each face of a truss'bay. The
diagonal has a folding hinge at its mid-length and locks-up
following deployment.
The hinge angles are designed So that when fully packaged, as
it would be in the cargo bay, the members are stress free. Also,
when fully deployed, the members are stress free. However, during
deployment or retraction, the members deform considerably. This is
seen in the bottom portion of the chart both in the bending and
twisting moments of the longeron.
i
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4B0
z
W
380
x
288
r%
180
upper triahgle
upper triangle •
ion Z
lower triangle
fully Packed fully T)eployed
20
...... 1-ELEMENT
......... 2-ELEMENT
4-ELEMENT
i:., 0
, 7"
zo -20
/ _ -60
I--
0 30 60 98
LONGERON ANGLE
I I i
O 30 60 90
LONGEROM ANGLE
i00
LATDYNSimulation of Controlled Robotic Slewing
Operation on Space Station
The LATDYN code is used to simulate Space Station
response to a i0 degree slew of an RMS-like arm carrying a 32,000
pound payload. The slew operation is performed very slowly,
taking 80 seconds. (At this rate a complete 360 degree operation
takes about the half an orbit of the station.)
A torque motor at the arm's root drives the operation and,
using angular rate feedback, suppresses the arm's vibration. As
shown in the figure, the simulation provides the torque history
which can then be used to improve the design of the torque motor,
gimbal, or truss members. Also provided is the resulting module
micro-gravity environment which shows that even though the arm
controller suppresses arm vibration, as seen in the torque
history, the modules continue to ring for a long time. Clearly
more is required if the module micro-gravity environment _s to be
further reduced.
OF-2
10° Slew of 32000 Ib
In 80 Seconds
• Perform 10 ° slew using RMS-like arm
• Torque motor control law performs slew and
suppresses payload vibration
• Generate torque history for future loads analysis
• Examine micro-g environment
400 --
,o-
6 o
=o-
o -400I-,-
lJ_
_. -_0Q,
.1200 = I , I = I , I , I L_--,40 80 120 160 200 240
Time, sec.
p 31.1
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U
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0
3 6.2
0 40 80 120 160 200 240
Time, sec.
i01
Potential CSI Test Article
A potential CSI article is depicted in the first of the next
three charts. Though not shown to scale, the truss contains ten
inch cubic bays. In the LATDYN simulation, the larger antenna,
labeled B, is rotated 30 degrees about the vertical y axis (yaw
rotation) and the response at the truss center of gravity is
studied under two conditions; without an attitude control system
and with an attitude control system.
In the absence of an attitude control system, the yawing of
the antenna produces a yaw of the spacecraft due to conservation
of angular momentum and a roll of the spacecraft due to the offset
of the antennas from the truss-beam neutral axis. In addition,
gyroscopic effects result in a smaller pitching motiQn of £he
craft. Angular feedback control on the motor which drives the
antenna yaw helps to suppress some of the ensuing vibrations. Its
design being based on rigid body assumptions, it does a poor job
of this.
In the presence of an attitude control system, the overall
attitude of the spacecraft is kept along its nominal path, but
vibrations of the flexible craft are Significant. Additional
actuators are necessary to reduce these vibrations.
Antenna A Y
Antenna B L_ - -- -, "
_'vF/_" / , J J• f• •
20.32 m
104
SPACECRAFT RESPONSE AT TRUSS C.G. DUE TO 30 DEG. LARGE
ANTENNA YAW - WITH ATTITUDE CONTROL
B
? 2 iv,, ,
/Ro_
I ,/A ^
x
-4
0 10 BO B@ 40
Time, Secs.
SPACECRAFT RESPONSE AT TRUSS C.G. DUE TO 30 DEG. LARGE
ANTENNA YAW - WITHOUT ATTITUDE CONTROL
A
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0
.FI
0
_
-2-
-4-
-S
t,,A ---'"' "°'
Yaw
0 5 10
Time, Secs.
105
!=
Requirements for Multibody Benchmark Experiments
The next two charts address the need for multibody
experiments which can be used to determine their accuracy and
reliability. Such experiments should be relatively inexpensive and
easy to assemble and to change out components. Most importantly
their motions when rigid components are used must be significantly
different from their motions when flexible components are used.
One such experiment is shown It consists of three nearly
rigid members and one pendular member which can be either rigid or
flexible. Response of the pendular member tip is shown both for a
flexible and a rigid member. The responses are desirably
different, even having a somewhat different fundamental frequency.
The dimensions of the members and the tip mass have been
chosen so as to make the device stable, but these can be changed
to come as close as desired to instability. This represents an
important test for simulation codes, since they may predict
stability when the system is unstable or stable when it is not.
o INEXPENSIVE
o EASY TO ASSEMBLE AND CHANGE COMPONENTS
O FLEXIBLE MOTION SIGNIFICANTLY DIFFERENT FROM
RIGID BODY MOTION
106
FLEXIBLE PENDULUM MULTIBODY EXPERIMENT
03
LL
>_
"3
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>
c-
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r',j
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-1-
t-
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///
' / /
,1/
/ / t
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rigid
I , I , I ,
S
Time, Secs.
flexible
107
CONCLUDING REMARKS
O MULTIBODY RIGID/FLEXIBLE COUPLED EXPERIMENTS ARE REQUIRED
FOR SIMULATION VALIDATION
o THOUGH COST-EFFECTIVE RELATIVE TO EXPERIMENTS, SIMULATION _:
OF SPACE VEHICLE OPERATON REQUIRES EXPENSIVE COMPUTER RUNS
o LATDYN VERSION AND DOCUMENTATION SOON TO BE RELEASED AND
WORKSHOP TO BE HELD
L L
1o8
|
!
REFERENCES
i. Housner, J. M., McGowan, P. E., Abrahamson, A. L., and Powell
M. G., The LATDYN User's Manual, NASA TM-87635, January 1986.
2. Housner, J. M.,"Convected Transient Analysis for Large Space
Structures Maneuver and Deployment", AIAA/ASME/ASCE/AHS 25th
Structures, Structural Dynamics and Materials Conference, AIAA
Paper No. 84-1023-CP, Palm Springs, California.
3. Housner, J. M., Wu, S. C., and Chang, C. W.,"A Finite Element
Method for Time Varying Geometry in Multibody Structures",
Proceeding of the AIAA/ASME/ASCE/AHS 29th Conference,
Williamsburg, VA, April 18-20, 1988, pp.187-197.
4. DADS User's Manual, Computer Aided Design Software, Inc., P.O.
Box 203, Oakdale, Iowa 52319, 1987.
5. Wu, S. C., and Haug, E. J.,"Geometric Non-linear Substructuring
for Dynamics of Flexible Mechanical Systems", International
Journal for Numerical Methods in Engineering, Vol. 26, pp.2211-
2226, 1988.
6. Adams, L. R.,"Design, Development and Fabrication of A
Deployable/Retractable Truss Beam Model for Large Space
Structures Application", NASA CR-178287, June 1987.
109
2_S


Controlled multibody dynamics simulation for large space structures

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