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Control of Uncertainties within an Interdisciplinary Design Approach of a Robust High Heel
L. Mosch
mosch@sfb805.tu-darmstadt.de
Technische Universit¨
at Darmstadt
Department of Computer Integrated
Design, Petersenstraße 30
64287 Darmstadt, Germany
S. Adolph, R. Betz,
J. Eckhardt, A. Tizi
gleichstellung@sfb805.tu-darmstadt.de
Technische Universit¨
at Darmstadt
Department of Mechanical Engineering
Petersenstraße 30
64287 Darmstadt, Germany
J. Mathias, A. Bohn
mathias@sfb805.tu-darmstadt.de
Technische Universit¨
at Darmstadt
Product Development and Machine
Elements, Magdalenenstraße 4
64289 Darmstadt, Germany
K. Habermehl, S. Ulbrich
habermehl@sfb805.tu-darmstadt.de
Technische Universit¨
at Darmstadt
Department of Mathematics
Dolivostraße 15
64293 Darmstadt, Germany
Control of Uncertainties within an
Interdisciplinary Design Approach of a
Robust High Heel
Within this paper the combination of several methods, developed and used in Collaborative
Research Center (CRC) 805 – “Control of Uncertainties in Load Carrying Systems
in Mechanical Engineering” of the DFG (German Research Foundation), is used to
demonstrate the development of a load carrying system under uncertainty. The development
starts with the identification of relevant uncertainties, followed by a conceptual design
and a mathematical robust optimization approach. The optimized structure is used for
the layout of a 3D-CAD-model which is used to print a real rapid-prototyping-model.
Throughout the whole design process uncertainties are considered. To demonstrate the
symbiosis of these methods an example is chosen. Usually, CRC 805 deals with load
carrying systems in mechanical engineering. To let this topic become more vivid and to
show that the methods can be transferred to other fields, the design of a robust high heel is
taken as an example. At the end of the work three high heels are developed and evaluated
regarding their robustness against uncertainties.
Keywords: uncertainty analysis, robust design, robust optimization, visualization, high
heel
Introduction
In load-carrying structures uncertainty is caused by several
influencing factors like unknown usage, variation in material
properties, deviation in production processes, unknown information,
etc. Those uncertainties need to be considered in the development
process of a product. Controlling uncertainties in load-carrying
structures has furthermore the potential of minimizing safety factors
and avoiding over-sizing. This leads to economic advantages,
saved resources and the extension of application areas. Therefore
uncertainties are identified, described and evaluated in a process
model to control them by various methods and technologies. To
control uncertainties in load carrying systems, such as chassis,
bicycles or truck-mounted cranes is the aim of Collaborative Research
Center (CRC) 805 – “Controlling uncertainty in load-carrying
structures of mechanical engineering”. Within CRC 805 several
research areas are involved to analyze and control uncertainties in
all phases of the design process. Uncertainty occurs when process
properties of a system cannot be determined (Engelhardt et al., 2009).
Uncertainties mainly refer to deviations of properties, which occur
during the product life cycle’s processes. To identify uncertainties it
is important to consider the whole product’s life cycle. Within this
work, products that are generally insensitive against uncertainties are
called robust products. To achieve a robust product several methods
can be applied. The systematic exertion of these methods is regarded
within this paper and it describes the interdisciplinary collaboration
of mechanical engineers and mathematicians. To demonstrate the
combination and interaction of the methods, a concrete example is
chosen. The task is to develop a high heel which is unsusceptible
against arising uncertainties in the production and the usage of the
Paper received 1 May 2012. Paper accepted 23 August 2012.
product. Additionally, the methods developed in science could be
connected and verified in a practical project. The design of the
high heel and the linking between the models and methods will be
displayed with intermediary results of each design phase. The work
starts with the analysis of the usage processes of a high heel and
identification of relevant uncertainties, e.g. the angle of the applied
load, unknown user-weight or the knuckle angle. The entity of the
identified uncertainties is the basis for the conceptual design and first
simple sketches of the high heel. Abstracting into a truss topology
design model allows the usage of a mathematical robust optimization
approach. The optimized structure is used for the layout of a 3D-
CAD-model. The work finishes with realistic rapid-prototyping-
models of the designed high heels and an evaluation of three different
high heels regarding their robustness compared to a standard high
heel. At the end of this paper one high heel is chosen which meets
the requirements best regarding uncertainties.
This idea was part of a competition, called ”Achilles High Heel”
for female and male students guided by the Gender equality team of
CRC 805, which was motivated by gender equality issues.
Nomenclature
A(v)= stiffness matrix
cf= compliance for given load f
fs∈Rn= loading scenarios
Uf= uncertainty set for loadings
U∆= polyhedral uncertainty set
U◦= ellipsoidal uncertainty set
v∈Rm= bar volumes
Vf= displacement space
Vmax = maximal volume
x∈Rn= displacement vector
J. of the Braz. Soc. of Mech. Sci. & Eng. Copyright c
2012 by ABCM Special Issue 2, 2012, Vol. XXXIV / 597
Mosch et al.
Superscripts
m = number of possible bars
n = degrees of freedom
S = number of scenarios
Uncertainty Identification
At the beginning of each design process it is necessary to clarify
the design task. In this case the task is to develop a robust high
heel. First of all, an abstract definition of a high heel has to be given.
Afterwards the relevant uncertainties need to be identified.
Definition and description of a high heel
In the context of this paper the high heel is an open lady’s shoe
with a heel height of at least 100 mm (approximately 4 inches), Fig. 1.
Insole, outsole and seat describe the massive parts where the foot is
placed. The heel, the top piece and the sole under the toe box transfer
the force induced by the user’s weight to the floor.
Figure 1. Basic definition of a high heel.
Robustness and uncertainty in the context of a high heel
A robust product ”maintains a stated performance level of its
properties in spite of fluctuations in primary and secondary inputs,
the active environment, the operands and in human operation”
(Andersson, 1996). In the meaning of the CRC 805, the entity
of fluctuation is called uncertainty. As basis for a robust high
heel design the occurring uncertainties need to be identified. It is
obvious that the angles of the knuckle and the floor are important
uncertainties occurring during the usage of a high heel. But there
are other important uncertainties, e.g. sweat or the constitution
of the floor which can influence the behaviour. A more or less
complete identification of relevant uncertainties is supported within
a systematic uncertainty analysis. To analyze uncertainties within
the CRC 805 an Uncertainty Mode and Effects Analysis (UMEA)
is developed (Engelhardt et al., 2009). With the application of this
method occuring uncertainties and their effects should be identified,
prioritized and calculated. Nevertheless the accomplishment is
connected with certain effort. Given that the synthesis of a robust
product is the main goal, the analysis of uncertainties is executed
in a reduced way. Nevertheless the reduced way is based on the
application of a process model (Kloberdanz et al., 2009) which is the
basis of the UMEA. Using this model the relevant uncertainties can be
identified. The knowledge of these uncertainties is the initial starting
point for the development of a robust product.
Process model as basis for identification of uncertainties
In its simplest way the process model is based on a graphic
visualization of a timeline in form of a labeled arrow. By
parallel and sequential assembling and back coupling of several
processes, the model chains and networks of processes can be
described graphically. With the help of this structured division of
process chains subprocesses can be regarded in more detail by the
engineer. Uncertainties which occur within a separate process can
be determined. Basically, the process model facilitates the engineer’s
communication and understanding of the usage processes. The results
of the process modeling and the analysis of uncertainties constitute
a conjointly aligned foundation for further steps of the design. At
this point the process model arranges for a simple and quickly
understandable documentation of the analysis results. For the design
of a robust product the identified uncertainties are crucial. Within the
design process these uncertainties must be controlled.
Identification of uncertainties of a high heel
Figure 2. Uncertainty analysis based on a process chain model.
Figure 2 shows the usage processes that typically occur when
using a high heel. Afterwards these processes are prioritized (white,
orange and black bubbles) to detect the most important processes
(black). It is necessary to keep this step manageable and to
concentrate on the main processes. Therefore the analyzed processes
need to be reduced to a manageable number. The processes a high
heel is usually faced with and are supposed to be the most important
uncertainties are marked with black. The less important processes
are marked with white. Usage processes which can occur but are
not important are not marked at all, e.g. sitting. Therefore it is
not necessary to analyze these processes in a detailed way. The
important processes need to be analyzed carefully. Figure 2 also
shows one process (dancing) with identified uncertainties in detail.
Uncertainties which can occur while dancing are for example wet
or plain floor, broken glass, exudation, impulse and abrasion. These
uncertainties can be dangerous for the person wearing the high heel
and can probably lead to serious injuries. Therefore, it is important
to design a high heel that is immunized against these uncertainties.
Other processes are analyzed similarly. At the end of this design
step a table including the identified and prioritized uncertainties can
be created. The named uncertainties are standardized and not entire.
Table 1 provides the basis for the design of a proper solution.
598 / Vol. XXXIV, Special Issue 2, 2012 ABCM
Control of Uncertainties within an Interdisciplinary Design Approach of a Robust High Heel
Table 1. List of identified uncertainties influencing a high heel.
Standardized uncertainties/disturbance
1. Soil condition
1.1 Plain floor
1.2 Porous floor
1.3 Bulk floor
1.4 Soft floor
1.5 Humidity
2. Exudation
3. Angle
3.1 Sidewise angular attaching
3.2 Sidewise angular attitude
3.3 Longitudinal angular attitude
4. Loading
4.1 Weight
4.2 Batches
4.3 Deviation
5. Foot anatomy
6. Shoe abrasion
6.1 Internal sole abrasion
6.2 Sole abrasion
Conceptual Design
In this step a conceptual solution for the design task is searched.
Due to the robustness which is regarded as the most important
requirement in this step a solution should be found to control the
individual uncertainties. Principal concepts are deduced which
control all identified uncertainties.
Search strategies and order pattern to design a robust concept
A basic possibility to control an uncertainty is the adding of a
function within the product. This function is aligned particularly
to control the uncertainty. This approach is obvious and easy to
understand. On the basis of this approach a search for solutions can be
carried out directly. Solutions can be found which can be integrated
within the product. Certainly, this results in high efforts since for each
uncertainty an additional solution is necessary. Moreover, interactions
between several uncertainties and their solutions are neglected when
using this approach. Despite these disadvantages this simple approach
of adding a function is used. It directly leads to a creative and
exciting intuitional search for solutions. This way of searching
solutions is suitable when working in a creative and design-oriented
team and therefore, it was suitable as a task for the competition
Achilles High Heel. Especially, in connection with Robust Design
the intuitive search for solutions can be supported systematically
throughout certain strategies. Herewith, a guided intuitive search is
carried out to come across suitable solutions as soon as possible.
Basically, these strategies are based on the identification of the so
called search fields. In these search fields it seems to be possible that
an uncertainty occurs. Then products or ideas can be identified, which
are robust for these search fields. Typically, these solutions cannot be
assigned to the own design task directly because solutions are always
dependent on the product. Therefore they are not suitable for a new
design task. At first it is necessary to understand how the solution
can control the uncertainty to derive an abstract principle. Using this
principle, measures regarding the own design can be derived.
To discover new search fields which are interesting for controlling
uncertainties three strategies can be defined:
“Related Products” strategy: Search for related products and
identify which uncertainties they are usually faced with. Identify
principles of controlling and assign them to your product.
Explanation: Solutions can be recognized quite easily in products
that have a similar body but differ in their intended use. To find these
products the engineer can set up a catalogue which contains every
related product he knows and investigate the products concerning the
occurring uncertainties. The advantage of this strategy is that the
found solutions are quite close to an applicable solution for the own
design task. Therefore solutions can be assigned easily and with little
effort. Partially, for the assignment it is not necessary to work out a
control principle.
“Related Environment” strategy: Search for environments
where the regarded uncertainty usually occurs. Identify products
which are robust in these environments and identify principles of
control. Assign these principles to your product.
Explanation: Typically, special environments and special
application areas ask for special requirements for technical products.
These products control occurring uncertainties in a special way
and can be used to identify the basic approach of control. If found
products are not coincidentally related, the engineer must have a high
ability for abstraction to recognize and deflect assignable principles
for his own development task.
“Biological Principles” strategy: Search for natural
environments where the uncertainty that must be controlled
usually occurs. Identify biological creatures which exist inside these
environments. Identify the principles of control and assign them to
your product.
Explanation: Within nature many uncertainties can be controlled
through proper solutions. On the basis of known uncertainties a
sort of uncertainty-scenarios can be expressed. By means of this
scenario biological environments can be searched which are similar
to the scenario. Solutions that are developed by biological creatures
within this environment can be used in terms of principles to realize
a technical implementation. Today this technical implementation
is known as bionic solution (Nachtigall, 2010). But today bionics
rather shows the cleverly implementation of a biological principle
into a bionic principle. As a real creative director for controlling
activities the biological principle is more suitable than the bionic
principle. The multiplicity of existing bionic solutions shows that
this approach basically works. Furthermore, nature shows that very
often several uncertainties can be controlled through one clever
solution. Therefore this strategy can be used to find a solution which
can control several uncertainties conjointly and thus effectively.
Although this strategy at large basically offers a very interesting
approach, some difficulties can be identified. At first, the engineer
has to find out which biological environment is in accordance with
his environment. Afterwards he has to know the existing creatures.
Therefore this strategy is only limitedly suitable for the application
through an expert of a technical field. Rather biologists should deal
with the application of this strategy. Partly the borderline of science
is reached when it is known that an uncertainty is controlled, but the
solution is not known or cannot be explained. Some examples of
these principles are given below.
J. of the Braz. Soc. of Mech. Sci. & Eng. Copyright c
2012 by ABCM Special Issue 2, 2012, Vol. XXXIV / 599
Mosch et al.
Solution strategies for a robust high heel
The principles described in the previous section are exemplarily
applied to the high heel designing task. Only a small number of
examples will be given. The solution scheme in Fig. 6 gives an
impression of the wide range of possible solutions.
•Example to “Related Products” strategy: The strategy of
“Related Products” is realized through the comparison to a
soccer shoe. A soccer shoe provides support and comfort for
its carrier; properties which a high heel should possess. This
is realized by robust support of the heel, since the ankle was
identified as the major vulnerability. Additionally, a ravel is
integrated into the sole to support the comfort. Wearing high
heels implies a partially insecure support, which results from the
minimal walking surface. Usually, the only connection between
a high heel and the ground is the small area of the heel as well as
the sole under the toe box. To provide a stable hold similar to a
sneaker, the high heel shows a conical shaped walking surface,
which connects the heel with the plateau.
Figure 3. “Related Products” example.
•Example to “Related Environment” strategy: An orthopaedic
splint enhances the stability of an injured leg and prevents from
twisting one’s ankle. It is difficult to integrate a splint into a
shoe because of aesthetic aspects. The designed high heel meets
both requirements. The “Related Environment” strategy is used
in the context of soil condition, e.g. wet, stony, soft or diagonal
ground. Depending on the condition, resulting uncertainties and
derived requirements are formulated.
Figure 4. “Related Environment” example.
•Example to “Biological Principles” strategy: The “Biological
Principle” is realized by using the example of an elephant foot.
An elephant foot forms a circle, which consists of tendons and
fat. Putting the foot on the ground, the foot area enlarges and
forms a large walking surface. Lifting the foot, the surface area
contracts again. This phenomenon can be transferred to the high
heel. In this case the surface area is represented by the heel and
its top piece. This function meets the requirement of a stable
foothold and simultaneously fulfils the aesthetic standards.
Figure 5. “Biological Principles” example.
Uncertainty solution scheme
After this step partial solutions for every important uncertainty
can be generated. These solutions can be seen in figure 6, which
shows an uncertainty solution scheme (see Pahl an Beitz, 2007). It
contains the uncertainties horizontally and the ideas for solutions
vertically. By analyzing this table, synergy effects can be seen when
combining several partial solutions. By using this table the engineer
can try to find combinations of partial solutions which are able to
control several uncertainties simultaneously.
Figure 6. Uncertainty solution scheme for a robust high heel.
To demonstrate the search simply and clearly it is helpful to use
the solution scheme in terms of a morphological approach. Here,
every uncertainty is related to different possibilities of control in a row
of a matrix. Thus, in the first column the uncertainties which need
to be controlled are shown. In the fields of every row the solutions
are shown which are basically supposed to control the uncertainties.
These solutions are shown in the fields in terms of simple sketches.
These sketches can be understood very easily and quickly. Moreover
they offer a simple overview. This scheme can be used by the engineer
to develop concepts that can answer the development task. Firstly, the
scheme can be analyzed systematically by means of suitable questions
to identify problems and potentials easier:
•Are there unfilled rows? It is possible that within the scheme
there are rows which don’t contain solutions. In this case a new,
more intensive search has to be accomplished. If an intensive
search is already accomplished it has to be proved whether it is
possible to leave the uncertainty uncontrolled without provoking
a reduction of robustness.
•Are two or more rows widely identical? If there are rows
where widely all solutions coincide, it has to be checked
whether both uncertainties coincide as well. Partly, uncertainties
that are basically identical can be regarded as different during
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Control of Uncertainties within an Interdisciplinary Design Approach of a Robust High Heel
the analysis. In this case the uncertainty can be described
consistently and the redundant row can be deleted. Otherwise
the uncertainties can be combined because no solution is lost
when deleting one of the rows.
•Do solutions exist which control several uncertainties? In this
case this solution offers a high potential to control several
uncertainties with little effort.
•Can two or more solutions be combined or are they similar?
Even in this case it is supposed that several uncertainties can be
controlled with reduced effort.
By using these questions the engineer can reduce the field of
solutions and find notably interesting solutions. However it is the
engineer’s main task to gather notably interesting concepts through
clever combinations and avoiding conflicts.
The concept’s demonstration takes place as a simple sketch
which is the typical tool for product development. Additionally, it
appears that some control approaches are not easy to be demonstrated
graphically. In these cases a short additional description is carried out.
When the combination via the uncertainty solution scheme is
finished, a conceptual design containing several partial solutions can
be generated. An example for this step is shown in Fig. 7, a sketch
of a high heel which is robust against several uncertainties. Due
to its broad sole the shoe is robust against porous, soft or bulk
floor simultaneously. At the same time it has a high plateau against
humidity and a heel similar to a spring to realize the robustness against
batches and to balance the person’s weight. Other uncertainties are
controlled similarly by other properties. After this step a first sketch
of a robust high heel is generated and the step of conceptual design is
finished.
Figure 7. Conceptual design sketch.
Robust Optimization
Now that a design concept of the high heel is found, we are
interested in the optimal design of the high heel. We want to use
mathematical methods to find an optimal design. For load-carrying
systems several approaches are known that can optimize a load-
carrying structure for given loadings (see Bendsoe and Sigmund,
2003), e.g. free-material optimization, topology derivatives or truss
topology design.
Robust optimization of load-carrying structures
Since in the case of optimizing a high heel under uncertainty,
whose loading especially is uncertain, we decided to apply the
concept of truss-topology design, where the concept of robust
optimization with uncertain loading parameters is well-understood
(see Ben-Tal and Nemirovski, 1997) in contrast with other known
methods where the problem of uncertainty in the parameters is either
hard to handle or appropriate concepts are not known.. In truss-
topology design a ground structure consisting of nodal points (some
of them are fixed, the others define the displacement space Vfwith n
degrees of freedom) and mpossible connections between these nodes
is given.
Figure 8. Left: ground structure of a truss, right: optimal design after truss
topology design.
For a given load f∈Rnthe aim is to find the optimal bar volumes
v∈Rm, such that the compliance cf=1
2fTxis minimal. The vector
x∈Rndescribes the displacement of the free nodes obtained via
Hooke’s Law (A(v)x=f) with A(v)∈Rnxn being the stiffness matrix
of the truss described by bar volumes v. This leads to the following
optimization problem :
min
v∈Rmd1
2fTx
s.tA(v)x=f
s.t
m
∑
i=1
vi≤Vmax
s.tv≥0
(1)
The two last constraints guarantee that the total volume of the
material of the structure is less than a given limit Vmax and the bars
have a positive volume v≥0. As explained before, the parameters
(especially the load f) are uncertain. A typical problem in truss
topology design is a result which is optimal for a given load f
but unstable for a slightly different loading e
f(see Ben-Tal and
Nemirovski, 1997).
Figure 9. Left: optimal truss for a given loading scenario, right: not stable
for small disturbance loads.
Therefore, the approach of robust optimization is used, which
minimizes the worst-case compliance over all loading scenarios f∈
Uffor a given uncertainty set Uf. This leads to the following model
of robust truss topology design:
J. of the Braz. Soc. of Mech. Sci. & Eng. Copyright c
2012 by ABCM Special Issue 2, 2012, Vol. XXXIV / 601
Mosch et al.
min
v∈Rmmax
f∈Uf
d1
2fTxf
s.t.A(v)xf=fs.t∀f∈Uf
s.t
m
∑
i=1
vi≤Vmax
s.tv≥0
(2)
The question now is, how to describe the uncertainty set Uf?
There are mainly two approaches - a polyhedral and an ellipsoidal
uncertainty set. The polyhedral approach is also called multi-load
truss-topology design, since the polyhedral uncertainty set U∆
f=
f:f=∑S
s=1λsfs,s.t∑λs≤1,s.tλs≥0can be described via a
finite number of loading scenarios {f1,..., fS}. This Multi-load-
formulation becomes a large-scale problem if a full-dimensional
uncertainty set for the n-dimensional displacement Vfspace shall be
considered, since S=2nscenarios are needed. Another approach is
based on an ellipsoidal uncertainty set U◦
f={f=Qu :||u|| ≤ 1}and
leads to the semidefinite problem formulation (SDP):
min
v,τ
τ
s.t.2τI QT
Q A(v)0
s.t
m
∑
i=1
vi≤Vmax
s.tv≥0
(3)
For details, especially on the definition of the matrix Q∈Rqxn see
Ben-Tal and Nemirovski (1997).
Robust optimization of a high heel
To apply robust truss topology design to design and optimize
a robust high heel, an abstract ground structure of the high heel is
necessary, consisting mainly of nodes (free and fixed) and bars. For
this purpose, about 100 nodes are determined to represent the high
heel abstractly. These nodes are linked through about 3000 bars
to represent the possible material of the shoe. The abstract ground
structure can be seen in Fig. 10, on the left. Based on this abstract
ground structure several loading scenarios are applied which represent
the prioritized processes found in the uncertainty analysis. For each
process loading scenarios fs∈Rn(with n≈300 degrees of freedom)
are chosen, which represent the chosen process:
•f1: standing (700 N orthogonal to the ground equally distributed
on all nodes of the whole sole)
•f2: standing on the ball of the foot (700 N orthogonal to the
ground distributed only on the top nodes of the plateau)
•f3: slipping (combined forces parallel to the sole structure)
•f4: dancing (tilted forces in important nodes, e.g. at the seat, at
the top or at the passage between plateau and insole)
•f5: dipositioned foot (700 N slightly tilted to the orthogonal
loads)
These loading scenarios are the basis for the uncertainty set,
which is completed by additional small disturbance loads. In this
case, an ellipsoidal uncertainty set is chosen with
Uf={f=Qu :kuk≤1}(4)
with Q=f1;··· ;f5;σe1;··· ;σeq−5∈Rn×q, a robustness factor
σ>0 and an orthogonal basis e1,...,eq−5in the orthogonal
complement to the subspace spanned by the forces {f1,..., f5}in Rn.
When the uncertainty set is defined, robust truss topology design
can be used to receive the following optimal robust design, see
Fig. 10, on the right.
Figure 10. Left: ground structure of the abstracted high heel, right:
optimized high heel after robust optimization.
The result is an optimal truss which provides information about
the optimal material allocation. Since the design of a high heel aims
to be most aesthetical, which means finely wrought, we are interested
in a design which uses as sparse material as possible. The optimized
structure is the design with the fewest material needed to control the
given uncertainties. But of course, a designer might prefer a somehow
different design.
Visualization of Uncertainties in CAD-Models
The visualization of uncertain product properties is given in a
CAD-system. Part of this concept is the methodology of parametric
and knowledge-based design. The identified uncertain product
properties resulting from manufacturing are mapped on the modeling
parameters of the CAD-model. Constraints between parameters
present dependencies between uncertain product properties and allow
visualizing the effects and chain of effects. This potential allows a
variation of geometry in the lowest and highest border of the given
value of deviation and the resulting effects. The resulting parametric
CAD-model structure can be used for furthermore simulations. For
more details on parametric and knowledge-based CAD-design see
Mosch, Sprenger and Anderl (2011). The design of the high
heel, which is deduced by a mathematical optimization process, is
created as a CAD-model. All the prioritized functions to meet the
requirements are visualized and integrated in the model.
Figure 11 shows the finished model of three different design
approaches of a high heel. It is noticeable that the counter is
extremely high to support the hold of the heel. The top piece and
the plateau are linked together and result in a dynamic form. The sole
design provides a large walking surface, which decreases the potential
for uncertainty caused by different soil conditions. In total three
different design solutions are created, which are assessed regarding
their robustness against the identified uncertainties. These designs
are modelled in CAD-programs like Siemens PLM NX and Catia.
These CAD-models are the basis for printing realistic 3D-models via
rapid-prototyping techniques.
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Control of Uncertainties within an Interdisciplinary Design Approach of a Robust High Heel
Figure 11. CAD-models of three different designs.
Results and Conclusions
For the development of a robust high heel the combination of
several methods has been used to find a proper solution which can
control as much uncertainties as possible. At the end of the project
several designs of a high heel were found. In Fig. 12 the rapid-
prototyping-models of the designed high heels are shown.
Figure 12. Real RPT-models.
In Fig. 13 the shoes are evaluated regarding their robustness
against the identified uncertainties. One high heel can be identified
which meets the requirements and controls the uncertainties best.
The standard high heel in the upper left square is not suitable to
control all uncertainties, since the main focus is on the design but
not on the robustness against uncertainty. The shoe in the lower
left square controls the relevant uncertainties on a high level. Two
other solutions are generated which can control the uncertainties on a
higher level than the standard shoe, but they are also worse than the
lower left square shoe. To empower the high heel to control as much
uncertainties as possible the design apparently differs from standard
high heels.
Outlook
The applied methods are based on static loads. These methods
can not capture dynamic loads. The application of dynamic loads
especially of uncertain dynamic loads and other time dependent
uncertainty (e.g. degeneration, abrasion) is due in future work. The
team of CRC 805 focusses on dynamic aspects of uncertainty in the
near future and an enlargement of the used methods on dynamical
methods can be expected. Also the addition of real usage processes
shall be covered. In this work, we stopped at the production of
prototypes, which cannot be worn by test persons. This can be part
of a future project where the back coupling of usage process and
development process can lead to further interesting insights.
Acknowledge ments
The development of a high heel was a student’s project guided
by CRC 805 – “Control of Uncertainties in Load Carrying Systems
Figure 13. Radar chart for assessing the robustness of different high heel
designs (upper left square: standard high heel).
in Mechanical Engineering” and was motivated by gender equality
issues. The project was set up to increase the interest of young female
and male academics for the topic of uncertainties in load carrying
systems. We thank the German Research Foundation (DFG) for the
financial support.
References
Andersson, P. , 1996, “A Process Approach to Robust Design in Early
Engineering Design Phases”, Department of Machine Design Lund Institute
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