Lightweight Design Optimization of a Bow Riser

Transcription

Bow Riser Design Optimization in Olympic Archery / 33
European Journal of Sport Science, vol. 4, issue 3
©2005 by Human Kinetics Publishers and the European College of Sport Science
Lightweight Design Optimization
of a Bow Riser in Olympic Archery
Applying Evolutionary Computing
Jürgen Edelmann-Nusser, Mario Heller, Steffen Clement,
Sandor Vajna, and André Jordan
Recurve bows that are used in competitions like the Olympic Games are hightechnology products. Good risers are lightweight but retain a high stiffness. The
aim of this study was to design a riser with a stiffness comparable to that of the
lightest riser currently used by the archers of the German National Archery
Team, but with a considerably reduced weight. We computed the loads that are
applied to a riser of a drawn recurve bow (the RADIAN model used by the
German team) and created a 3-D solid CAD model of a riser with 24 variable
parameters. We used evolutionary computing to optimize the 24 parameters of
the model according to these criteria. We selected the most optimal riser out of
the 1650 CAD models generated, manufactured it, and had it tested by three
archers of the German National Archery Team. The mass of our manufactured
riser is 871g, which is 243g or 22% less mass than the RADIAN riser.
Key Words: Archery, evolutionary computing, optimization, sports equipment
design
Key Points:
1. We optimized a CAD model of a riser of a recurve bow for mass and stiffness using
evolutionary computing.
2. The evolutionary computing process was applied to an initial CAD model which
we developed using 24 variable parameters inspired by the design of the RADIAN
riser.
Dr. Jürgen Edelmann-Nusser studied Sports Science and Electrical Engineering is
with the Department of Sport Science at the Otto-von-Guericke-University Magdeburg. His
main fields of research are sports equipment, computer science in sports, swimming and
archery. Mario Heller is with the Department of Sport Science at the Otto-von-GuerickeUniverstity Magdeburg. Steffen Clement is scientific assistant of the chair of Information
Technologies in Mechanical Engineering at the Otto-von-Guericke-University Magdeburg.
His main fields of research are Autogenetic Design Theory and Integration of Calculation and
Design. Prof. Dr.-Ing. Sandor Vajna VDI, has 12 years of experience within industry on
research & development, management, consulting, and international lecturing on integrated
product development, design methodology, CAD/CAM, business & engineering process
reengineering and engineering systems integration and is holder of the chair of Information
Technologies in Mechanical Engineering at the Otto-von-Guericke-University Magdeburg.
André Jordan is scientific assistant at the chair of Information Technologies in Mechanical
Engineering. His main fields of research is Evolutionary Optimization in Product Development.
33
34 / Edelmann-Nusser, Heller, Clement, Vajna, and Jordan
3. We manufactured the most optimal riser generated, and had it tested by archers
from the German National Archery Team, who approved it.
4. Our riser had a stiffness comparable to the RADIAN riser, and was lighter by nearly
250 g.
Introduction
During the few thousand years that bows have been used, bows have changed from
simple wooden sticks to high-technology products. Today there are many different
kinds of bows used for different purposes. In the Olympic competitions, the recurve
bow is used. Figure 1 shows the major components of a recurve bow: its limbs, riser
and stabilizers. In competition, some additional small components, such as a sight,
are necessary.
Most risers are manufactured in two different sizes: 23 inch (58.4cm) and 25
inch (63.5cm). In the 2000 Olympic Games, all archers on the German National
Team used one of the 25 inch risers manufactured by Hoyt (see Figure 2).
A good riser is typically lightweight but has a high degree of stiffness (4). The
current trend in riser design has been to reduce weight. For the past twenty years,
most risers have been made of aluminum alloys. The first risers were massive
designs and therefore very heavy. Today, risers are made with lightweight designs
such as those shown in Figure 2.
We asked whether current riser designs, especially the design of the RADIAN
riser, really represent the best lightweight designs, or whether it would possible to
considerably reduce the weight of a riser. Our inquiry was not solely inspired by the
Figure 1 — Components of a recurve bow. The limbs are flexible and store the energy.
The riser is stiff and made of metal. The stabilizers damp the vibrations after the shot.
The limbs are attached to the riser by snapping the limb butts into the limb pockets of
the riser.
Figure 2 — Three 25’’ risers of the Hoyt company (USA) with a lightweight design (side
view and front view). From left to right: the models RADIAN, AVALON, and AXIS.
The lightest riser is the RADIAN with a mass of 1114g. The masses of the AVALON and
AXIS are 1154g and 1374g, respectively. Other risers made by this company are the
MATRIX (1245g) and the AEROTECH (1302g).
current trend to reduce riser weight. An empirical study shows that increasing the
mass of a bow by 200g results in a significant larger range of motion of the bow
during aiming, even after training (2). A larger range of motion during aiming
correlates to a poorer score (2). Hence we can assume that a decrease in mass of the
bow will influence the interaction between archer and bow in a way that may
produce a better score. And this would be a plausible result: during an Olympic
competition or a World Championship, an archer who achieves the finals must shoot
more than 200 times in one day. A lighter weight would reduce archer fatigue.
Another indication that a desirable riser should be lightweight comes from the
reaction of competitive archers to a new product offered by Hoyt. Before the AXIS
model was manufactured, many archers of the German National Archery Team used
the RADIAN. As promoted by the manufacturer, the AXIS riser is stiffer than the
RADIAN. After some tests of the AXIS, most of the archers of the German Team
declined to change from the RADIAN because of the AXIS’ higher weight.
The goal of this study was to produce a 25 inch riser with a stiffness comparable to the RADIAN riser, the lightest riser in use by archers of the German National Archery Team, with a considerably reduced weight.
Methods
The methods used consist of the following four parts:
1.
2.
3.
4.
An analysis of the loads that are applied to the riser of a drawn bow.
A static structural analysis of the riser RADIAN using the loads of point 1.
Design of a parametric CAD model of the riser
Optimization of the parameters of the CAD model using evolutionary
computing.
The analysis of the loads
During aiming, when a bow is drawn, it can be assumed that there is a static balance
of forces. Figures 3, 4 and 5 show the external and internal forces in play. The
constraints for the static balance of forces of a drawn bow are shown in equations (1),
(2), and (3):
(1)
(2)
(3)
with:
(4)
(5)
Figure 3 — Drawing of a drawn bow with the external forces FA (draw weight) and FH
(force of the hand that holds the bow) that are applied to it and the internal forces FS
(string forces). LA: draw length; LW: length of the limbs of the drawn bow; LM: length of
the riser.
Figure 4 — Drawing of the internal forces of a limb of a drawn bow. The mounting of the
limb at the limb pockets is modeled as a floating bearing (bearing A) and a thrust
bearing (bearing B). The names of the angles and the force FS (string force) correspond
to Figure 3.
The objective here is to compute the forces FAs, FBs and FBp as functions of the
draw weight FA and of the geometric and trigonometric variables of Figures 3 and 4.
This results in the equations (6), (7) and (8):
(6)
(7)
(8)
Limb and limb pockets are standardized so that limbs and risers of different
manufacturers can be interchanged. Limbs are available in three different sizes:
short, medium and long. The combination of these different limb sizes with 23 inch
(58.4 cm) or 25 inch (63.5 cm) risers results in bow lengths that are within a range of
62 inches (157.5cm) up to 70 inches (177.8 cm) (see 5). The value of the variable a in
Figure 4 is 75mm for all limbs. We used a bow with a 25 inch riser and long limbs to
get the values of the other geometric and trigonometric variables in order to compute
the forces FAs, FBs and FBp according to the equations (6), (7), and (8). The bow was
drawn with 71cm, 76 cm and 81cm draw lengths, and the values of the geometric and
trigonometric variables were measured. Long limbs were used to get a larger value
Figure 5 — Forces that result in loads of the riser of a drawn bow (compare Figures 3
and 4).
of LW that results in larger values of the forces FBS and FAS in the equations (7) and (8).
A 71cm draw length was used to approximate a 28’’(71.1cm) draw length, which is
the shortest draw length used for bows that have a 70 inch bow length, according to
Hoyt’s manual (see 5). Table 1 shows the forces FAs, FBs and FBp as well as the
geometric and trigonometric values for the three different draw lengths at a draw
weight of 200 newtons (200N).
This 200N represents a relatively high value for the archers of the German
Team. The Hoyt manual (5) specifies a draw weight of 152N if a 25’’ riser with long
limbs is used. We used 200N to delineate a safety range for the subsequent structural
analyses. Because the shortest draw length LA of 71cm results in the greatest values
of all three forces FAs, FBs and FBp (see Table 1), this 71 cm draw length is also used for
safety purposes.
The static structural analysis of the riser RADIAN
Based on a three-dimensional scan of a 25 inch RADIAN riser, a 3-D solid CAD
(Computer Aided Design) model was created, using Pro/ENGINEER 2001 software. Materials testing, such as bending tests, atom emission spectroscopy, and
scanning electron microscopy, was performed upon a 25 inch RADIAN riser to
obtain information about its Young’s modulus, yield point, the composition of its
aluminum alloy, and the production process of the aluminum alloy. Table 2 and
Table 3 show the results of this materials testing.
The static structural analysis was done using Geometric Element Analysis
(GEA), a process similar to Finite Elements Modeling (FEM), by using Pro/
MECHANICA software. A value of 72 GPa was assumed for the Young’s modulus,
the median of the range shown in Table 3. As loads were applied to the riser, the
forces FAs, FBs, FBp and FH=FA (see Figure 5) at a draw length of 710mm were
calculated according to Table 1.
Table 1 Three Different Draw Lengths LA of a Bow with a 25’’ Riser and
Long Limbs, the Forces FAs, FBs and FBp and the Trigonometric and Geometric
Variables According to the Figures 3, 4 and 5 at a Draw Weight FA of 200N
LA
[mm]
710
760
810
a
c
LW
[mm] [mm] [mm]
a
b
d
22.5°
25°
27°
22.5°
24°
26°
34°
36°
39°
75
86
545
FA
[N]
FAs
[N]
FBs
[N]
FBp
[N]
200
1583
1503
1462
1729
1646
1604
216
189
169
Table 2 Alloying Additions of a Riser RADIAN (mean values of five analyses
using atom emission spectroscopy); the composition corresponds to the
Material AlMg1SiCu (see Aluminium-Zentrale, 1995)
Addition
%
Addition
%
Si
Fe
Cu
Mn
Mg
0.713 0.3814 0.2958 0.0749
Zn
0.921
Sn
Ti
B
Cd
<0.001
0.0246
0.0013
0.0015
Ni
Cr
0.1251 0.0046 0.3086
Na
Sr
Zr
0.0035 <0.0005 0.0048
Pb
<0.01
Al
97.14
A dynamic structural analysis was not performed, because a study by Gros (3)
demonstrates that the stress induced in the bow by releasing the shot exceeds the
stress caused by drawing the bow by only about 5%—and that this 5% excess exists
for less than 10 milliseconds.
Figures 6 and 7 show the results of the three-dimensional static structural
analysis.
The maximum value of the stresses is 135N/mm_, the maximum value of the
displacements is 1.85mm, and the mass of the riser is 1048g. This differs from the
actual mass of the RADIAN (1114g) because the Radian riser includes three steel
bushings used to connect the stabilizers to the riser. These steel bushings were not
included in our model.
The design of a parametric CAD model of a riser
We then designed a 24-parameter CAD model based upon the CAD model obtained
from the RADIAN riser. Figure 8 shows our CAD model and 12 of the 24 parameters
used
Table 3
Mechanical characteristics of the riser RADIAN
Material production
process
Precipitation hardening
of AlMg1SiCu
density
[g/cm3]
yield point Rp0,2
[N/mm2]
Young’s modulus
[kN/mm2]
2.77
< 400
69-75
Figure 6 — The CAD model shows the stresses that result from the forces FAs, FBs, FBp
and FH=FA at a draw length of 710mm (compare Table 1 and Figure 5). The colors
encode the values of the stresses in N/mm_ according to the scale top right. The maximum value of the stresses is 135N/mm_.
Figure 7 — The CAD model shows the displacements that result from the forces FAs, FBs,
FBp and FH=FA at a draw length of 710mm (compare Table 1 and Figure 5). The colors
encode the values of the displacements in mm according to the scale top right. The
maximum value of the displacements is 1.85mm. The displacements were computed
relatively to the point of the load incidence of the force FH in Figure 5.
Figure 8 — Four side views of the parametric CAD model. 12 parameters of the 24
parameters are drawn in exemplarily. The Figure was created using randomized values
of the 24 parameters. A pattern consists of two triangular elements; i. e. there are four
patterns above and three patterns below the grip.
We chose to use an aluminum alloy used in aircraft industries as the material
for the optimization of the riser. This alloy, AS 28, is similar to AlMgSi1. Table 4
shows the alloy additions of AS 28. The density of AS 28 is 2.71g/cm_, its yield
point is 403N/mm_ and its Young’s modulus is 72GPa.
Optimization of the parameters of the CAD model
using evolutionary computing.
In evolutionary computing, populations of artificial individuals are created (compare 6, 7, 8). Each artificial individual is represented by a chromosome. The artificial individuals reproduce like biological individuals, creating new artificial individuals. To perform an optimization, the artificial individuals are evaluated (compare
9), and the fitness of each is calculated with respect to the optimization parameters.
Artificial individuals which are more fit are more likely to reproduce. Operations
such as crossover, mutation and recombination can be performed on the artificial
individuals.
In our case, the artificial individuals evaluated were computer models of
risers. Each model riser was represented by its “chromosome” consisting of our 24
individual parameters. The program used all three techniques of recombination,
mutation, and crossover in causing the model risers to reproduce. New model risers
Table 4
Alloying Additions of AS 28
Addition
Si
Cu
Mn
Mg
Zn
Ti
Zr
%
0.9
0.3
0.6
0.9
0.1
0.06
0.12
Addition
Cr
others
Al
0.15
<0.15
96.8
%
were thus created. The fitness of each new model riser was defined according to its
fitness value. To get the fitness value for each model riser, the stresses and the
displacements were computed according to Figures 6 and 7. On the basis of these
stresses and displacements, the fitness fi of each model riser was calculated using
equation (9).
(9)
with:
a, b, c, d ...
fi
mi
max, i
s,i
weighting factors
fitness (quality) of the riser i
mass of the riser i
maximal value of the displacements of the riser
standard deviation of the stresses of the riser i
In this equation, the mass is the criterion for the desired lightweight quality,
and the displacement is the criterion for the desired stiffness quality.
To calculate fi, we also used the standard deviation of the stresses to eliminate
risers with a too-large variance in the stresses. We did not use the maximal value of
the stresses because the maximal value of the stresses could be assumed to be much
lower than the yield point of the material: maximal value of the stresses in Figure 6 is
135N/mm_ ; the yield point in Table 3 and for AS 28 is about 400N/mm_. Therefore,
we assumed that the maximal value of the stresses would not be a problem.
Figure 9 shows a schematic diagram of the evolutionary computing. The
algorithm can be explained in the following eight steps:
Step 1: The algorithm starts with 31 individuals that are initialized with randomized values.
Step 2: The 31 individuals are evaluated on the basis of the analyses of stresses
and displacements. The fitness value fi of each individual is calculated (see equation
no. 9). The fittest individual is selected.
Step 3: Using a roulette-wheel selection, 15 couples (parents) are linked
together to be used for reproduction. Roulette-wheel selection means that the probability for each individual to be selected is proportional to its fitness value fi (see 8).
In such a selection, it is possible for an individual to be selected more than once and
to be coupled with itself.
Step 4: The 15 parents recombine with a probability of 80% according to the
method “uniform order based crossover” and create two children each. There is a
20% probability that the parents’ traits will not recombine, and that the “children”
produced are in fact clones of a parent.
Step 5: For each of the 30 children, there is a 5% probability that one randomized parameter out of the 24 will mutate. In the case of a mutation, the actual value of
that parameter is changed to a uniformly distributed value within the range of the
parameter.
Step 6: For each of the 30 children, there is an 0.8% probability that all 24
parameters will be reinitialized with randomized values.
Step 7: Once this is done we now have the next generation of 31 individuals
consisting of 30 children and the old best individual (generation i+1 in Figure 9).
Each of these 31 individuals is evaluated on the basis of the analyses of its stresses
and displacements according to Figures 6 and 7, and the fitness value fi of each
individual is calculated (see equation no. 9). The new fittest individual is picked out.
Step 8: go to step 3. Repeat for all successive iterations.
Figure 9 — Schematic diagram of the evolutionary computing. The algorithm starts
down right with 31 individuals that are initialized with randomized values. “pb” means
“probability” More explanation to the Figure see in the accompanying text.
The algorithm stops after a pre-defined number of loops or generations. We
did two runs of this algorithm using different weighting factors (see equation 9) and
different numbers of generations to stop the algorithm (see Table 5).
When finished, we short-listed the ten individuals identified as having the
best fitness values out of all of the generations of both runs, to be tested in making the
final selection of the riser that would be manufactured and then tested by the archers.
In this final selection we added three criteria to the criterion fitness value fi:
• The maximal displacement should not be much larger than the maximal displacement of the riser RADIAN—i.e., it should be less than 2mm.
• The displacements of the upper and lower limb pocket should be approximately the same—i.e., there should be some kind of symmetry in the displacements (see Figure 10).
• There should be a minimum of torsion in the riser, especially at the upper limb
pocket (see Figure 10).
Table 5 Weighting Factors and Numbers of Generations for the Two Runs
of the Evolutionary Computing
Run no.
a
b
[1/kg]
c
[1/mm]
d
[mm_/N]
Numbers of
generations
1
2
50
50
70
50
4
4
0.4
0.4
20
35
Figure 10 — Displacements of the upper (on the left) and lower (on the right) limb
pockets of the riser RADIAN. The colors encode the values of the displacements in mm
according to the central scale. The maximal displacement at the upper limb pocket is
1.42mm, at the lower limb pocket 1.85mm. On the left side we see that there is torsion at
the upper limb pocket.
The riser that we finally selected was manufactured with forged AS 28 using a
CNC (computerized numerical control) milling machine. The first practice tests
were conducted at the Olympic Training Center in Berlin by three athletes of the
German National Archery Team. Two athletes shot nine times each; the third athlete
shot 300 times.
Results
Figures 11 and 12 show the masses and maximal displacements of the risers that
were created in the two runs of the evolutionary computing. We see clearly that the
mass of the RADIAN riser is very large compared to the masses of the risers created
by the evolutionary computing. We also see in Figure 12 that there even are risers
with less mass and less maximal displacement. As mass was given a lower weighting factor (see Table 5) in the second run, the selection pressure changed to individuals with larger masses and smaller maximal displacements. This resulted in a shift of
the scatter plots to the top and to the left if we compare Figure 11 with Figure 12. This
change in the selection pressure also leads to different mean values of the masses
and different mean values of the maximal displacements between the individuals of
the first and of the second run. In the first run (see Figure 11) the mean value of the
masses is 864g and the mean value of the maximal displacements is 2.74mm. In the
second run (see Figure 12) these values are 880g and 2.63mm, respectively.
The riser that was selected for manufacture according to the fitness value fi and
the additional three criterions described above is marked with a blue rhomb in
Figure 12. Figure 13 shows a computer model of this riser; Figure 14 shows its
displacements; Figure 15 shows the displacements of its upper and lower limb
pockets (compare Figure 10); and Figure 16 shows the stresses.
Figure 11 — The black rhombs mark the mass and the maximal displacement of each
individual of the first run with 20 generations. The red circle marks the mass (1048g)
and the maximal displacement (1.85mm) of the riser RADIAN for comparison. Not all
individuals are included in the Figure for there were individuals with a maximal displacement of more than 5mm or a mass of more than 1050g.
Figure 12 — The black rhombs mark the mass and the maximal displacement of each
individual of the second run with 35 generations. The red circle marks the mass (1048g)
and the maximal displacement (1.85mm) of the riser RADIAN for comparison. The
blue rhomb marks the riser that was selected for manufacturing. Not all individuals are
included in the Figure for there were individuals with a maximal displacement of more
than 5mm or a mass of more than 1050g.
Figure 13 — CAD model of the riser that was manufactured. Its mass is 869g, its
maximal displacement is 1.94mm and the maximal value of its stresses is 160N/mm_.
Figure 17 shows a photo of the manufactured riser. Its total mass, including
three HELICOIL threaded inserts for the connection of the stabilizers, is 871g. It is
243g lighter than the RADIAN riser (1114g).
Figure 18 shows on the left side a complete bow with the new riser; on the right
we see an archer of the German National Archery Team testing the riser.
In the shooting tests, the three archers were asked to tell us their subjective
impressions of shooting with the new riser:
All stated that the new riser suits them: It is not only stiff and light, but also
damps the vibrations after the shot very well. The archer who shot 300 times also
told us that the bow groups shots well. In this context, “to group well” means that, if
Figure 14 — The CAD model shows the displacements that result from the forces FAs,
FBs, FBp and FH=FA at a draw length of 710mm (compare Table 1 and Figure 5). The mass
of the model is 869g (riser RADIAN 1048g). The colors encode the values of the displacements in mm. The maximum value of the displacements is 1.94mm (riser RADIAN:
1.85mm). The displacements were computed relatively to the point of the load incidence
of the force FH in Figure 5.
Figure 15 — Displacements of the upper (on the left) and lower (on the right) limb
pockets of the new riser. The colors encode the values of the displacements in mm. We
see that the maximal displacements at the upper and lower limb pocket have almost the
value of 1.94mm. On the left side we see the torsion at the upper limb pocket (compare
Figure 10).
Figure 16 — The CAD model shows the stresses that result from the forces FAs, FBs, FBp
and FH=FA at a draw length of 710mm (compare Table 1 and Figure 5). The colors
encode the values of the stresses in N/mm_. The maximum value of the stresses is 160N/
mm_ at a yield point of 403N/mm_.
Figure 17 — Photo of the manufactured riser. Its mass is 871g.
the archer thinks that an arrow should hit the target next to the hit of another shot, the
arrow really will hit the target in that spot–that is, the archer perceives that the
variance in the hits results from the variability in his or her muscle control, and not
from some mechanical slackness of the bow. Furthermore, the 300-shot archer
asked to use our new riser in the next season’s competition.
Discussion
Figures 11 and 12 show that the RADIAN riser is in no way optimized for mass or
stiffness. Evolutionary computing creates risers with less mass and less maximal
displacement (see Figure 12). Thus we can assume that if we had increased the
selection pressure in some manner to get less displacement, we would have seen a
(a)
a
(b)
Figure 18 — (a) Complete recurve bow. (b): Archer of the German National Archery
Team testing the riser.
shift of the scatter plot in Figure 12 to the left and to the top. Quite a few risers could
have been created with less mass and less maximal displacement than the RADIAN
riser.
In Figures 11 and 12 we also see that it is possible to design risers with a mass
of less than 800g, if we will accept maximal displacements up to 4mm. The problem
is that we do not really know how reduced stiffness will influence archers’ shooting.
Though the literature gives high stiffness as a criterion of a good riser, and trainers
and archers also believe this to be true, there are no empirical studies supporting this
opinion. When we consider the degree of displacement of the flexible limbs when
the archer draws the bow, which can be 700, 800 or 900 mm, it seems implausible
that the one, two, or three millimeters of variance in the maximal displacement of
different risers could really influence the shooting. A more plausible criterion could
be torsion, especially torsion of the upper limb pocket. If the torsion is too great,
when the shot is released, the arrow can be accelerated not only in its axial direction,
but also in a direction orthogonal to its axis. As a result, the arrow does not fly
straight on to the target but skids a little bit to the side. This would negatively affect
both the shot and the score.
Our selection of a riser with a maximal displacement of 1.94 mm was therefore conservative, reflecting the current standards of the sport. Even so, our riser’s
mass is nearly 250g lower than the mass of the RADIAN.
In further empirical studies, it would be interesting to manufacture the riser
derived from the evolutionary computing that had the smallest mass (779g) but a
maximal displacement of 3.53 mm (see Figure 11), and to compare it against our
manufactured riser.
Conclusion
We achieved our goal of designing a riser with a considerably reduced weight yet a
stiffness comparable to the RADIAN riser. The evolutionary computing created
many risers and we selected the best one, according to our present criteria. But we
cannot assume that our riser really is the absolutely best optimal riser, because our
optimization was based on 24 parameters, which we defined according to considerations of plausibility and practicability; and which were inspired by the design and
shape of the RADIAN riser. Equation no. 9, used to compute the fitness variable fi, is
based upon similar considerations. Hence, an experiment using different parameters, a differently-shaped riser, or a different equation to compute the fitness variable could lead to different and perhaps better results. Furthermore, we only investigated the use of aluminum alloys for manufacture. Other materials could also prove
useful.
For these reasons, we are currently conducting a further study with a completely new design, including a differently-shaped riser, using magnesium alloys.
We chose magnesium because its density is only 1.8g/cm_. The problem with using
magnesuim alloys is that the Young’s modulus of these alloys is only about 40 kN/
mm_. We therefore do not know whether we can reduce the mass to less than 870g
and yet achieve a similar stiffness compared to our manufactured riser, made of AS
28. Fig. 19 shows a preliminary CAD model of a riser made of magnesium. This
model is not yet optimized for mass and stiffness, but demonstrates its approximate
shape.
Figure 19 – CAD model of an riser made of a magnesium alloy.
Acknowledgments
The authors gratefully acknowledge the supplies and the technical discussions offered
by Dr. Doris Regener from the Department of Materials and Materials Testing of the Ottovon-Guericke University Magdeburg. The authors also wish to thank the German Federal
Institute of Sports Science (Bundesinstitut für Sportwissenschaft, Bonn, Germany, project
no. VF 0408/15/40/2003) for their support in the manufacturing process.
References
1. Aluminium-Zentrale e. V. editor. 1995. Aluminium-Taschenbuch. Band 1: Grundlagen
der Werkstoffe. Düsseldorf: Aluminiumverlag.
2. Edelmann-Nusser J. 2003. Olympisches Bogenschießen, Methoden zur Untersuchung
und Ansätze zur Verbesserung der Funktionalität des Gerätesystems Bogen. In: Roemer
K, Edelmann-Nusser J, Witte K, Moritz F, editors. Sporttechnologie zwischen Theorie
und Praxis. Aachen: Shaker. p. 18-32.
3. Gros HJ. 1997. A training and feedbacksystem for archers. In: Wilkerson J, editor.
Biomechanics in Sports XV. Denton: TWU. p. 463- 69.
4. Haidn O, Weineck J. 2001. Bogenschießen: trainingswissenschaftliche Grundlagen
Balingen: Spitta. 416 p.
5. Hoyt. 2003. Recurve Bow Owners Manual. http://www.hoytusa.com /technical/images/
2003_Recurve_Manual.pdf. Accessed 2003 November 28.
6. Nilsson NJ. 1998. Artificial intelligence – a new synthesis. San Francisco: Morgan
Kaufmann. 513 p.
7. Pohlheim H. 2000. Evolutionäre Algorithmen. Verfahren, Operatoren und Hinweise für
die Praxis. Berlin: Springer Verlag.
8. Schöneburg E, Heinzmann F, Feddersen S. 1994. Genetische Algorithmen und
Evolutionsstrategien. Bonn: Addison-Wesley.
9. Vajna S, Clement S, Jordan A. 2002. Autogenetic design theory: an approach to optimize
both the design process and the product. In: Proceedings of the 2002 ASME Design
Engineering Technical Conferences September 29, 2002 - October 2, 2002, Montreal,
Canada. p 111.

Lightweight Design Optimization of a Bow Riser

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