by J.C. Raterink and S.M. Nooij, Taniq, and S. Koussios, Delft
University of Technology, The Netherlands
The design of pressurized filament wound structures is a wide-
spread and well-understood subject (refs. 5 and 8). A classical
item produced by means of filament winding is the well-
known isotensoid pressure vessel. It has found applications in
LPG tanks and inflatable bodies to jack up heavy loads in
crisis situations.
Design in engineering applications involve multiple disci-
plines that depend on each other. These are the shape, materi-
als, function and production process. The trend is to focus on
the improvement of the materials used. The Delft University
of Technology has developed Corpo fiber reinforcement,
which focuses on the shape. The Corpo technology considers
isotensoidal shapes that are stacked onto each other and are
overwound in an integral fashion.
This article introduces the Corpo technology and explains
its basic principles. There are three design parameters that
describe a Corpo shape. They influence the behavior of the
product and can be chosen for each individual application.
This patented technology is currently owned by Taniq, a
spin-off from Delft University of Technology. Taniq has fur-
ther developed the technology and applied it to improve the
products and production processes of its customers in the tech-
nical rubber industry. It has many advantages compared to
conventional design; the weight and durability of the product,
for example, can be improved. All these advantages contribute
to the reduction in costs, which is, of course, the driving factor
in the market nowadays.
Basic principles of the Corpo technology
Composites are materials made of two or more components.
By combining a matrix and a reinforcing material, high
strength to weight ratios can be achieved. The reinforcing
material, usually a kind of fiber, provides the strength and stiff-
ness. The matrix, usually with low strength and stiffness, pro-
vides air-fluid tightness and supports the reinforcing materials
to maintain their relative positions. These positions are of great
importance because they influence the resulting mechanical
properties (refs. 1 and 3).
Fiber path optimization is quite well known for straight
hoses and single bellow shaped products (ref. 8). A shape
where all fibers are equally loaded is called an isotensoid
shape. Isotensoid loading has many advantages. Firstly, the
performance of the fibers can be maximized throughout the
whole structure. In this way, the product can be made lighter
or sustain higher forces. Secondly, it can be designed in such a
way that the matrix material does not carry load (ref. 6). This
leads to zero shear stress in the matrix, improving the durabil-
ity of the product.
Taniq and Delft University have developed a novel tech-
nique for pressure vessels, called Corpo fiber reinforcement.
The technology considers isotensoidal shapes that are stacked
onto each other and are integrally overwound (ref. 7). This
integrally wound fiber path is geodesic, which means that the
fiber is running over the shortest path. As the geodesic path
is entirely determined by the underlying meridian profile, the
latter is designed in such a way that the fibers are equally
tensioned everywhere. Therefore, the structure is an isoten-
soid.
Design parameters
By combining the so called netting theory and the membrane
theory, a set of equations can be obtained that describe these
geodesic isotensoid fiber path shapes (ref. 4). With only three
parameters, q, r and ρ
0
, different meridian shapes can be cre-
ated. The meridian profile is then revolved to obtain a rotation-
ally symmetric body (figure 1). Multiple rotational symmetric
bodies can be stacked onto each other to increase the axial
length of the product.
The parameter q is approximately equal to the squared ratio
Improving the performance of fiber
reinforced pressurizable products
APRIL 2009
23
Figure 1 - revolving a meridian profile
to obtain a three-dimensional
Corpo shape (ref. 2)
p-axis
p
min
Z-axis
Meridian
profile
p
0
3D representation of the vessel
40 20 0 -20 -40 -40
-20
020
40
110
100
90
80
70
60
50
40
Figure 2 - different types of isotensoidal
shapes, with different q values, stacked
onto each other
RUBBER WORLD
Application of the technology
In this section, the wide range of possible applications of the
Corpo technology is outlined. First, existing conventional
products are introduced, and their problems and limitations are
discussed. After that, a tailored solution using the technology
is given for each subject.
Turbo hoses
Turbocharged engines incorporate turbo hoses to transport
compressed air between the air outlet of the compressor and
the inlet manifold of the engine. They must level internal pres-
sure and be flexible at the same time. To cope with increasing
pressure, the conventional approach is to add more material.
This has a negative effect on the flexibility. Another problem
of conventional hoses is that reinforcement rings are required
in order to maintain the bellow shape under internal pressure.
Figure 4 shows schematized principles of the production of
a conventional hose and a Corpo reinforced hose, respectively.
The fabrication does mainly rely on manual labor. First, rubber
sheet material is reinforced with fabric plies by means of cal-
endering. These plies are then wrapped around a steel or alu-
minium mandrel. Cotton tape is tightly wrapped around the
mandrel to compress the plies. The hose is then vulcanized
using hot air or steam. A large force is required to pull the hose
from the mandrel; this process is assisted by inflation of the
hose. Finally, the reinforcement rings are installed.
A Corpo reinforced turbo hose will keep its bellow shape
under pressure, eliminating the need for reinforcement rings.
Due to the optimized fiber geometry, up to 70% reduction of
fibers and 30% of rubber is possible. For this product, no weft
fibers and calendering are needed, which reduces the material
cost. Figure 5 shows a conventional turbo hose with reinforce-
ment rings and a Corpo reinforced turbo hose under produc-
tion. The production process of the Corpo structures can be
fully automated since it mainly relies on filament winding and
automated rubber placement.
Actuators
Actuators are used to induce movements and can replace pneu-
matic or hydraulic cylinders in a wide range of industrial ap-
plications. Conventional elastomeric air actuators such as lift-
ing bags and industrial air springs are reinforced by fiber plies.
These plies have a large contact surface in the cross-over points
of the maximum dimensionless radius (Y
eq.
) and minimum
dimensionless radius (Y
min.
) (figure 1):
Y
eq.
2
q =
(
)
Y
min.
(1)
Changing this parameter actually influences the degree of
concavity at the areas near the smallest radius (figure 2). Dif-
ferent products require different q; increasing the parameter q
leads to higher flexibility due to increased concavity. An off-
shore pipeline requires higher flexibility than a turbo hose, and
will therefore require a higher q.
The dimensionless load factor r is the ratio between the
axial resultant of the internal pressure on the projected surface
at the equator and a possible external axial force at the polar
ends:
k
a
r =
Y
eq.
2
(2)
where k
a
is a dimensionless coefficient. This coefficient is
calculated with:
A
k
a
=
pP ρ
0
2
(3)
where ρ
0
denotes the minimum shell radius, P the internal
pressure and A the external axial force on the structure. The
parameter r influences the axial length of the product. When r
is zero, the Corpo shape will not change in shape when pres-
surized. Choosing an r that is smaller than zero, the product is
able to withstand an external force in axial direction while
pressurized. To withstand this force on the structure, a positive
r should be chosen. For all configurations, the Corpo shape,
when pressurized, tends to go to its equilibrium position of r =
0. This means that a shape with a positive r will contract. Also,
the radius tends to decrease, which can be used as a clamping
force at the edges for a better sealing of the flanges. This favor-
able behavior can be used for compensators/expansion joints,
for which the sealing at the edges is critical. Different meridian
shapes with varying r are plotted in figure 3.
The profile is sized with the parameter ρ
0
, which was al-
ready introduced and stands for the theoretical minimum ra-
dius of a cell. It is a theoretical minimum, because for most
shapes, the actual minimum radius is slightly larger. When, for
example, the required radius of an end connection is known,
ρ
0
can be changed accordingly to make this connection fit.
24
Figure 3 - representation of meridians with
different r values plotted (ref. 7)
r = 0.5
r = 0
r = -0.25
r = -0.5(= -1/q)
r = -0.6
z
Y
p
0
p
0
r = 0.5
r = 0
r = -0.25
r = -0.5(= -1/q)
r = -0.6
Figure 4 - schematized principles of the
production of a conventional hose and a
Corpo reinforced one
Conventional reinforcement
of bellow shapes
Corpo reinforcement
of bellow shapes
APRIL 2009
25
which cause large stresses during expansion/contraction. The
induced stresses limit the maximum allowable pressure and the
lifetime of the actuator. There are already cylindrical elasto-
meric air actuators which allow exact prediction and control of
the movements due to controlled fiber placement. However,
applying the same principles for the reinforcement of complex
shapes, like a bellow, is more difficult and hardly known.
The advantages of these bellow shapes are that they provide
high forces in combination with large strokes and a minimal
deflation height. The properties of these complex shaped ac-
tuators can be improved using the Corpo technology. With
Corpo, the fibers are geodesically wound over the product in-
stead of using reinforced plies. These fibers follow the shortest
path and therefore do not need friction to stay in place. Because
of this fact and the absence of shear stresses in the matrix, the
maximum allowable pressure and lifetime are significantly
increased.
Expansion joint
Expansion joints are used to compensate the relative move-
ments in rigid piping systems. Because the conventional pro-
duction methods do not allow optimal orientation of the rein-
forcement material, a considerable amount of fiber and rubber
is needed to obtain the required strength. The unnecessary
material use results in a high wall thickness, leading to less
flexibility. Furthermore, without controlling the orientation of
the reinforcement, it is not possible to control the shape while
pressurized. This makes it more difficult to design and can lead
to failures resulting in loss of fluids or gas.
By using the Corpo technology to reinforce compensators/
expansion joints, these problems can be solved. The smart fiber
placement will increase the pressure resistance which can re-
duce the amount of materials needed; this leads to a slender,
more economical and flexible joint. Another advantage is that
the behavior under pressure can be predicted and controlled.
This increases the safety and also enables new functionalities
such as self-tightening ends for the flanges (figure 6).
Conclusion
In this article, we have presented the design principles and
some typical applications for the Corpo reinforcement technol-
ogy. Its optimized fiber geometry is obtained through geodesic
fiber paths on axially connected isotensoidal cells. Depending
on the required dimensions, shape and properties of the prod-
uct, the parameters r, q and ρ
0
can be chosen for a tailored solu-
tion. Parameter q influences the degree of concavity at the
areas near the smallest radi-
us. The dimensionless load
factor r is the ratio between
the axial resultant of the in-
ternal pressure and a possi-
ble external axial force at
the polar ends. The profile is
sized with the parameter ρ
0
,
which is approximately the
theoretical minimum radius
of a cell.
A comparison with exist-
ing conventional products
has been carried out to high-
light the advantages of this
technology. Improvement
Figure 6 - a
compensating hose
applicable for
offshore pipelines
made with Corpo
Figure 5 - a conventional (l) and a Corpo (r)
reinforced turbo hose
opportunities for turbo hoses, actuators and expansion joints
are hereby given. The main advantages include:
• Higher possible pressure levels;
• increased durability;
• lighter products possible (up to 70% reduction of fibers
and up to 50% in rubber);
• control of geometry;
• increased flexibility;
• cost reduction; and
• higher production automation.
It can be said that the performance and weight are related to
each other; either the same pressure levels can be obtained with
less material, or higher pressure levels can be reached with the
same amount of material. The reduction of materials automati-
cally results in cost reduction.
References
1. Beukers, A. and Hinte, E. van, “Lightness: The inevitable
renaissance of minimum energy structures,” Amsterdam: 010
Publishers, 1998.
2. Brevet, M., “Development of a mandrel for line production
of charge air cooler hoses with Corpo reinforcement,” Master
thesis, TU Delft, 2008.
3. Daniel, I.M. and Ishai, O., Engineering Mechanics of Com-
posite Materials, New York, Oxford: Oxford University Press,
2006.
4. Herkel, C. ten, “Integral geodesic winding in hose applica-
tions. Master thesis,” TU Delft, 2007.
5. Jong, de Th., (in Dutch) “Het wikkelen van drukvaten vol-
gens de netting theorie,” Report VTH-166. Structures and
Materials Laboratory, Faculty of Aerospace Engineering, Delft
University of Technology, Delft, April, 1971.
6. Koussios, S., Nooij S.M. and Bergsma, O.K., “Pressurized
structures and hoses: Improved structural performance and
flexibility through optimal fiber reinforcement.”
7. Koussios, S., “Filament winding: A unified approach,” PhD.
Thesis. Faculty of Aerospace Engineering, Delft University of
Technology. Delft University Press, 2004.
8. Vasiliev, V.V., Krikanov, A.A. and Razin, A.F., “New genera-
tion of filament-wound composite pressure vessels for commer-
cial applications,” Composite Structures 2003: 62: 449-459.
Dostları ilə paylaş: |