DESIGN EXAMPLE

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DESIGN EXAMPLE 1 Deployable Optical
TelescopeDesign challenges
A project of the US Air Force Laboratory
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Objectives

• To significantly increase the resolution of
  current space-based imaging, larger than the
  current Hubble 2.4 m diameter telescope are
  needed (about 6 m).
• Volume constraints new system must be stowed at
  launch, deployed in space.
• Lightweight constraint, high pointing accuracy,
  adequate stiffness, dimensional stability
• Carbon-fiber based composites are ideal
  candidates because of low TEC, high
  stiffness/weight.

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Project overview
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Project overview
The most difficult problem to solve is that of
deployment accuracy. Optical surfaces must be
shaped to a tolerance that is just a fraction of
the wavelength of the light being collected. In
practice, this condition requires that optical
surfaces have a tolerance of about ten nanometers!
The deployed segments must be placed relative to
each other with the same ten nm accuracy. This
requires precision structures, precision
deployment, highly linear hinges and highly
accurate latches. Typically, structures and their
deployment must be accurate to approximately 1
mm. The hinges and latches must be carefully
designed to perform linearly in both tension and
compression. Even so, absolute deployment to this
accuracy is impossible and fine adjustments must
be made after deployment to obtain and maintain
position. These adjustments require highly
sensitive sensors and actuators, as well as very
complex control algorithms to manipulate them.
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To obtain precise control, the overall deployed
system must be extremely light and stiff.
Stiffness to weight ratios, four times that of
the lightest space-demonstrated honeycomb
sandwich construction, are typical. This
requirement dictates the use of the most
advanced, stiff materials available, typically
ultra-high modulus graphite, as well as a
complete transformation in the way mirrors are
made. Rather than heavy monolithic polished glass
mirrors traditionally used in optical systems,
new innovative extremely thin mirror structures
made of beryllium, silicon carbide, or ultra thin
glass must be used. These mirror structures
require their own actuators, sensors, and control
systems to retain precise shape in the presence
of normal satellite disturbances. Finally,
advanced adaptive optics techniques are required
to process the raw image, as even the most
advanced structures and control technologies are
incapable of truly achieving optical tolerance.
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DESIGN EXAMPLE 2 Advanced composite flywheel

• Background
• Physical principles
• Stresses in a spinning wheel
• Isotropic materials (metals)
• Anisotropic materials (advanced composites)
• Energy stored
• The key issue radial stresses
• Novel flywheel

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FLYWHEELS - Background

• One of the oldest human inventions (potters
  wheel)
• Can help solve several problems
• The constant human increase in use of energy
• The impact of that use on environment
• How to store energy efficiently on a large scale
• How to provide compact units with competitive
  energy range and performance

• Until recently, not used in a wide range of
  applications because of cost, and because not
  enough energy could be stored for a given
  flywheel weight. Radical change with modern
  advances in materials technology.

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FLYWHEELS - Principles

• A spinning wheel stores mechanical energy, which
  can subsequently be taken out and put in again
  inertial energy storage device
• It has a disk/cylinder shape, various geometrical
  options

Heavy-rim wheel
Almost solid wheel
Thickened wheel
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STRESSES IN A SPINNING WHEEL
1. ISOTROPIC MATERIAL

• sr radial stress
• sq hoop (or circumferential) stress
• rotational angular velocity
• a, b internal, external radii

The radial and hoop stress distributions can be
calculated by using classical elasticity theory
for an homogeneous isotropic sold with boundary
conditions
sr 0 at r a sq 0 at r b
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The basic equation
The solution
EXAMPLE Aluminum disk density (r) 2.7
g/cc Poisson ratio (n) 0.33 b 20 cm, and l
a/b 0 (full disk) to 0.75 (open disk) w
1000 rad/sec
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No hole (full disk)
RADIAL
HOOP
DISPLACEMENT
When a hole is present at center (l ? 0), radial
stress is maximum in-between edges of ring hoop
stress is maximum at internal edge of ring,
minimum at external edge.
Tip speed bw 2pbn 200 m/sec (n number of
revolutions/time)
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SIMPLER VIEW
HOOP STRESS
RADIAL STRESS
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Of importance
The stresses in the flywheel increase as its
density (mass) increases, and as it spins faster.
In practice, a limiting value will be set by
the tensile strength of the flywheel material
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2. ANISOTROPIC MATERIAL Fiber-reinforced
composite materials are orthotropic materials.
They have dissimilar elastic behavior in
different directions. Thus, designing structures
with composites allows much more flexibility than
with metals or ceramics. But the math modeling is
more complex! Extension of previous stress
analysis for orthotropic flywheels
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ORTHOTROPIC MATERIALS
The basic equation
The solution (with same boundary conditions as
isotropic case)
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Interpretation and results for the orthotropic
case

• The stresses are proportional to the density (r)
• The stresses are proportional to the square of
  the tip speed (v)
• The stresses are completely defined by the
  material properties, radius ratio (l a/b), and
  speed w. In other words, there is no dependence
  on absolute dimensions of the ring.
• EXAMPLE A conventional graphite/epoxy composite

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No hole (full disk)
RADIAL
HOOP
DISPLACEMENT
As in the isotropic case, when a hole is present
at center (l ? 0), radial stress is maximum
in-between edges of ring hoop stress is (mostly)
maximum at internal edge of ring, minimum at
external edge.
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Effect of orthotropy
RADIAL
HOOP
Graphite/epoxy, l 0.5
Importance of orthotropy Material selection,
rotor dimensions, directions of reinforcing
fiber, etc, are all related to flywheel design.
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Carbon/Graphite fibers
Carbon fibers are manufactured by treating
organic fibers (precursors) with heat and
tension, leading to a highly ordered carbon
structure. The most commonly used precursors
include rayon-base fibers, polyacrylonitrile
(PAN), and pitch.
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Comparison of fibers and conventional materials
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ENERGY STORED IN A SPINNING WHEEL

• How do we calculate the energy stored in a
  spinning flywheel from the stress developed?
• The energy stored is given by
• I moment of inertia, t disk thickness
• But the mass of the disk is

Therefore the energy stored per unit mass, or
specific energy e, is
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But for a thin ring, a b and r b, and the
radial stresses are very small. The hoop stress
is
If the flywheel material strength in the q
direction is Xq, the theoretical ultimate
spinning velocity is
And for the specific energy
So, to achieve high energy storage with light
weight, rim material should be high-strength and
low density, which also implies high ultimate
speed.
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We now have all the necessary relationships for
designing a composite flywheel
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The problem of radial stresses

• Excellent specific energy performances are
  exhibited by thin rings only (thus, when a is
  close to b) see slides 5 and 11
• As the ring thickens (thus, as a/b decreases
  towards 0 for a full disk), the effect of radial
  stresses increases
• But radial performance of anisotropic composites
  is poorer than longitudinal (hoop) performance
• Radial strength governed by fiber surface
  treatment, fiber-matrix compatibility, fiber
  deterioration during manufacture, long-term
  interfacial performance (fatigue, polymer
  relaxation, etc).
• OBJECTIVES to reduce radial stresses to
  increase radial strength to modify stress
  distribution via a change in geometry and/or
  material, etc.

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Reduction of radial stress - strategies

• A large value of N (Eq/Er)1/2 results in lower
  radial stress. Therefore, a low modulus matrix
  (urethane, elastomer) is a way to obtain a thick
  ring with less transverse cracking.
• Second approach the multi-ring concept, with
  variable modulus, can change the stress
  distribution across the diameter

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Radial strength
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Example of improved flywheel design

• Multiring concept for radial stress reduction 5
  rings (Eglass/T300/T300/M40J/M40J, epoxy matrix)

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• As seen on the graph, the radial stresses
  between rings are below zero, therefore no
  split-up (fracture) of multi-ring. Also, radial
  stresses in each ring are predicted to be below
  transverse strength. Hoop stresses are below hoop
  strengths.
• Predicted peripheral speed v 1250 m/sec
• Stored energy U 1540 kJ 0.43 kW-hr
• Specific energy e 418 kJ/kg 0.12
  kW-hr/kg

NOTE 1 kW-hr 3600 kJ