Prof. W. H.
Warnes
Office: Rogers Hall 308
Phone and Voice Mail: (541) 737-7016
FAX: (541) 737-2600
This page last updated November 21, 1997
email:
warnesw@engr.orst.edu
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1) (60 points TOTAL) (65 points TOTAL) Part of the
proposed Space Station Freedom will be a set of laboratory
equip-ment for research into low gravity chemical and
materials processing. One piece of this equipment will be a
high speed centrifuge for separating solutions and applying
a centrifugal load to a specimen. The main arm of the
centrifuge, shown at the right, is fixed at a length of L,
but the cross sectional area, A, is free. Because of the
expense of launching equipment into space, minimizing the
mass is the most important objective. To function, the
centrifuge arm must also meet two constraints.
First, It must not fail under use, essentially a tensile
load of FTEST.
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Second, as the centrifuge starts to spin, it experiences an
inertial side load, which can be modeled as an end loaded cantilever
beam. The arm must not fail under the maximum side load, which is
expected to be FSTART.
The operative constraining equations are given below. Use these to
answer the following questions.
1.a) (5 points) What is the measure of
performance for this design?___________
1.b) (15 points) Derive the performance index
for the tensile (test) load constraint, M1, including the shape
factor if appropriate.
1.c) (15 points) Derive the performance index
for the side (start) load constraint, M2, including the shape factor,
if appropriate.
1.d) (10 points) Derive the coupling equation
for these two performance indices.
1.e) (15 points) In order to TRIPLE the
performance of the centrifuge arm under a side load, how large a
shape factor is required?
1.f) (5 points) Is this problem
underconstrained, overconstrained, or fully determined? Explain your
answer.
2) (15 points) Why are thermoplastic matrix
composites generally reinforced with discontinuous fibers?
3) (30 points)Define the following terms:
Rule of Mixtures:
Ceramic Whisker:
Sintering:
4) (15 points) Name three ceramic materials and
what group of ceramic materials they represent.
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SOLUTIONS
1.a) The measure of performance is MINIMUM
MASS: p = 1/m = 1/(rho L A).
1.b) For the tensile load constraint, there is
no shape factor because the tensile properties do not depend on the
cross sectional shape, only the cross sectional area.
1.c) For the side load constraint we do need
to worry about the shape factor. In this case, we are worried about
failure in bending, so the appropriate shape factor is phi(f-B).
1.d) 
1.e)
1.f) The problem is overconstrained because it
has two constraints, but only one free parameter.
2) Thermoplastic matrix composites generally use
discontinuous reinforcements (as opposed to continuous fibers)
because, even at high temperatures, the viscosity of the
thermoplastic materials isn't small enough to easily flow between the
continuous fiber reinforcements and fully "wet" them, filling without
void space. The discontinuous reinforcements allow for better
thermoplastic penetration and filling. An example is the use of
pultruded thermoplastics in automobiles for high strength, low weight
control consoles and dashboards.
3)
Rule of Mixtures: An
approximation for determining the properties of composites. The
property of the composite material may be approxiamted from the
properties of the components using
Pcomposite = VmPm + VrPr
where Vm and Vr are
the volume fractions of the matrix material and reinforcement
material, respectively, and Pm and Pr are the properties of the matrix and reinforcement
materials (see lecture notes).
Ceramic Whisker: A
reinforcement material used in composite materials that consists of a
ceramic single crystal, generally only a few microns in diameter and
up to a few millimeters long. They are used as a discontinuous
reinforcement (p. 129 Budinski and lecture notes).
Sintering: The fusing together of
powder particles (usually ceramics, but also for powdered metals and
some high temperature ploymers) by a high-temperature self-diffusion
process, usually under pressure (p. 193 Budinski and lecture notes).
4) Check the notes and Budinski for solutions.
Examples include:
Al2O3 is a member of the oxides;
TiC is a member of the intermetallics:
pyrolytic graphite is a member of the carbons.
End of File.