FINITE ELEMENT COMPARISON OF
SINGLE LAYER AND SANDWICH
LAYER TITANAL SKIS
by
HAAVARD HACHAAG ANDERSEN
for
E Mech 407 Spring 2016
INTRODUCTION
I have for many years had a great passion for skiing, growing up in the Swiss Alps and Norway
has inevitably lead me down that route. I have spent the last seventeen years of my life alpine
skiing and started cross-country skiing at the age of three. Throughout those years, I rarely gave
my skis much thought, as I was too young, and during growth bi-annual replacement of skis is
almost inevitable. However, upon moving to the United States for college, with my growth
plateauing, I wanted to invest in a pair of high-end skis that would last a long time. When
researching ski types and constructions I realized that it is a lot more complex than I originally
thought. I also noticed how numerous variations of similar technologies were often labeled and
advertised as major selling arguments, without necessarily showing any kind of comparative
research.
This brings me to my project, which is a finite element analysis of two of these similar
constructions. I wanted to model two different versions of a ski using the same dimensions and
designs, with the only difference being a second metal alloy layer. The sandwich style metal
alloy ski such as the pair I own, is the stiffest and most stable pair of ski’s I have personally ever
tested. This intrigued me and thus I wanted to see if this could be due to the titanal-sandwich
construction as advertised. By constructing a simplified model that focuses on this aspect of the
ski construction, and by simulating common loading during alpine skiing I hope to see clear
differences in flexibility in response to applied forces.
APPROACH
To start off I had to research the constructions of skis, and although a lot of technical information
is available, blueprints and dimensions are rarely available. Skis are actually fairly complex to
model, as some of the components can comprise of several constituents, and consider directions
of fibers, epoxy, and glues. Even the simplest designs usually include at least seven components,
including the base, the edge, the core, the sidewall and the top sheet. Because this is very time
consuming and several of these components appear the same in both of my models, simplifying
the model is necessary, while isolating the factors that I care about in my simulations. I decided
therefore to neglect the bottom layer and the edge as other than affecting the exact loading
results, trends can still be observed. I chose to include a wood core, as its variable thickness is
essential for the force distribution properties of the ski. This is placed on top of the bottom metal
alloy, and in one model is also covered in one layer prior to the polymeric top sheet. This
simplified model allowed me to more accurately design the ski, while still including the core
features for my analysis. I noticed that this simplification greatly affects the cross sectional
forces, as a lot of the stiffness comes from the sidewalls, the direction of the wood fiber matters,
and most skis also include smaller layers of glass and/or carbon fiber layers. Therefore I circled
in on the beam deflection caused by a load, as this can simulate impacts from jumps and bumps,
while also, although underestimating, can be used to show trends in load during turns, although
this neglects the cross sectional deflection caused by carving and applying the pressure on the
edge of the ski.
Furthermore I had to choose my materials appropriately, which also required certain
approximations. To start off, as mentioned, this project is on the structural function of using two
rather than one Titanal layer in the ski. At first glance I assumed that titanal was a titanium based
metal alloy, however this is not the case. Titanal is in fact a brand name for an aluminum alloy
produced by Austria Metall AG (AMAG), intended for use in construction of for instance skis. It
is an alloy that can be compared to aluminums in the 7xxx series such as 7075 T6, but is
advertised as a high performance alloy, which according to AMAG performs better than these
equivalents due to increased yield strength and elastic modulus. The top layer of the ski can use
several different materials and has little effect on the overall properties of the ski, I chose to use
polyamide as it is frequently used in the industry. The core of the ski is usually a combination of
woods and synthetic materials, often layered in a specific fashion. To be able to accurately get
the properties I needed, I decided to rather than applying a simple wood, would use some ski
core manufacturers own test results to assign the mechanical properties of the material. Bcomp is
an example of a manufacturer that builds ski cores and has extended technical information about
their product readily available. As I only care about what happens along the ski axis, I could
isolate some of the properties, as they are not uniform due to layers of wood layered with fibers
and glue. Using only the mechanical properties along the axis of the ski, lets me more accurately
test this dimension.
Elastic Modulus
Poisson’s Ratio
Mass Density
Yield Strength
72000
0.33
2820
580
bCore D200
220
0.29
190
20
Polyamide Type 6
2620
0.34
1120
103.65
Material
Titanal
With the model complete the next step is running simulations. In order apply pressure in
a realistic way I used Peter Federolf’s dissertation1 on carving ski simulation as a source. He
used both numerical methods and experimental data to establish conditions upon which he would
run his simulations on, which gives me some information to work with. As I am statically testing
the ski, the loading approximation due to snow deformation, can be very useful. This model
shows that as the ski moves forward, the shovel (front tip) of the ski is subjected to additional
pressure by the snow, with the tail (rear tip) balancing out these forces. This causes the front half
of the ski to become a loading zone, and the rear an unloading zone. With the normal pressure
distribution being a trigonometric curve, with the maximum centered underneath the boot and the
minimums at either end of the ski, this model shifts the pressure slightly to the front. This is
simulated by using a non-uniform pressure distribution, described as a function of y, the length
along the ski axis, with y = 0, 10mm off the center and using a second degree polynomial in
order to gradually decrease applied pressure throughout the part. The slightly off-set center
account for a slight shift towards the front, increasing the pressure relative to the rear. As the ski
is missing certain layers and very simplified, using actual established loading values isn’t
necessary. This would cause the ski to deform more than realistically possible, as these extra
1
Federold, P. (?) Finite Element Simulation of a Carving Alpine Ski.
layers inevitably stiffens the ski. To simulate the boot I set the binding face to be a fixed face,
this allows the bending outside this base to be accurate, while neglecting the actual distribution
of forces caused by applying pressure to the ski through a bolted binding mount.
Solidworks side view of Two Layer Model with applied non-uniform pressure
Solidworks side & front view of Two Layer Model
RESULTS
With two finished models, one which is 4-12mm thick and the other which is 2.5-10.5mm thick,
the first containing two titanal layers, I can move on to my simulations. After having applied
materials and constraints I moved on to the non-uniform pressure described in the approach. As
this was a comparative analysis, and not all the structural components of the ski are present, the
force used was not related to actual loading. I used a function that varies between 0 and 1.62 over
the range of 1780mm. This is then multiplied by a set value of 250N/m^2 at each point resulting
in about 90N applied total pressure over the axis of the ski.
The meshing of the models became an effortful task as the contact layering between what
at points is a negligible height component and the rest of the components, would fail. By
rerunning the model for several different mesh settings, and by applying mesh control for a
component in one of the models I eventually ended up with functionally meshing models, with
similar sized elements. For one of the models, even after successfully meshing, I had issues with
it not running due to an error caused by meshing elements to intersect. I re-meshed this object
until I found a mesh that would not get caught up in this error. Eventually both models ran
simulations fine. The time spent per mesh itself was about 20 seconds with slight variations
depending on the density, and the simulation spent between 15 and 25 seconds.
Shovel of Ski after Mesh (Two Layer)
The simulations yielded several different calculations and results, one of which is the
Von Mises stress. The Von Mises stress is a very useful way to determine how an object is
affected by the application of pressure or forces. Von Misses is a scalar value calculated for each
finite element, based on the three dimensional tensile/compressive stress and shear stress
described below.
Von Mises Stress general equation
This conveniently only describes the stress that will distort the shape, as when applying several
forces, some might cancel out.
Comparing the results for the two models depicted below, the Von Mises analysis shows
that the peak Von Mises, which is what we often look at in comparison to yield points of the
material, is noticeably higher in the single titanal layer ski. The maximum appears to occur on
the barrier between the fixed geometry and the flexible ski. This might be inaccurate in terms of
where the actual Von Mises peaks would be, but as the pressure is higher closer to the center,
and the ski thickness is at its highest points, with the majority of deformation happening in this
area, the results appear as predicted. The model with two titanal layers appears to have a lower
Von Misses peak than the one with one titanal layer. This is what I expected as the two layer
model would be stiffer and help distribute the forces along the ski axis while reducing the
deformation at this single point.
Von Mises Stress Distribution (Pa or N/m2) (Two Layer / One Layer)
URES is one way Solidworks can measure change in displacement. It is the mean of the
displacement along all axis, which in my case is mostly normal to the ski axis. This is because I
have no loading cross sectional to the ski, and only a minor contribution to the ski axis itself, due
to slight angles due to the camber of the ski, the tail, and the shovel. The results from this was as
expected, as the two layer ski appears stiffer and more resistant to displacement than the single
layer titanal model.
URES Displacement (mm) (Two Layer / One Layer)
Finally the last part of the simulation I looked at was the strain throughout the model.
Strain is the change in displacement over the length of the member, which in this scenario is
applied to every finite element in the model. Rather than expressing the overall displacement, it
measures the geometric response due to forces being applied. The values are again higher for the
single layer model than the two layer model. I believe that this is due to the second titanal layer
helping to distribute the forces along the axis of the ski, rather than having the majority
displacing the elements closer to the barrier of the fixed geometry.
ESTRN Strain (Two Layer / One Layer)
CONCLUSION
After having modeled two models, one with a titanal sandwich structure (above and below the
core), and one with a single bottom titanal layer, I found fairly expected but interesting results. It
appears that the two layer structure is a lot stiffer, as it deforms less upon applied forces than the
single layer model. It specifically seems to distribute the load more equally along the length of
the ski, reducing the deformation at single points. This is a property that can be useful in a ski as
stiffness allows the user to be less affected by inconsistencies in surface. This can be related to
speed limits experienced by the user, although this has been shown to be more affected by
torsional vibrations in the ski.2 For continuous progress, the most important thing to do is to try
to maintain the structural integrity of the ski, by including all constituents and its material
properties. By modelling a proper ski binding and using common mounting practices, the load
exerted on the ski from the user would be a lot more accurate. This would allow the ski to be
somewhat flexible underneath the foot, giving a more precise depiction of the distributed forces
throughout the ski. If the model is accurate enough, considering directions of fibers, epoxy and
other macroscopic material properties, I would be able to analyze cross axial yielding, which is
necessary to simulate the edging of a ski during a turn. Furthermore, a more accurate model
would allow me to test for buckling and other non-comparative values and actually pinpoint the
skis yielding under normal loading conditions rather than some referential value. Finally, as
vibrations are very important especially when approaching the speed limit (of the user or the
skis), different frequency tests could tell me more about the skis tendency to become unstable,
which is rooted in this.
2
Foss, G. C., Glenne, B. (2007) Reducing On-Snow Vibrations of Skis and Snowboards.
BIBLIOGRAPHY
Foss, G. C., Glenne, B. (2007) Reducing On-Snow Vibrations of Skis and Snowboards.
Retrieved from http://www.sandv.com/downloads/0712foss.pdf on April 20, 2016.
Federolf, P. (2005) Finite Element Simulation of a Carving Alpine Ski. ETHZ. (16065)
Retrieved from http://e-collection.library.ethz.ch/eserv/eth:28070/eth-28070-02.pdf on April 19,
2016.
CAPINC. (2014) Frequently asked questions on Von Mises Stress Explained. Retrieved from
https://www.capinc.com/2014/02/12/frequently-asked-questions-on-von-mises-stress-explained
on April 22, 2016.
Folsom Skis. (?) Creating Custom Skis. Retrieved from
http://www.folsomskis.com/construction/ on April 19, 2016.
Bcomp. (2013) bCore D200 Technical Data Sheet. Retrieved from
http://www.bcomp.ch/files/bcore_d200_tds.pdf on April 20, 2016.
AMAG. (?) AMAG Titanal. Retrieved from https://www.amag.at/en/our-aluminium/sportingconsumer-products/sporting-goods/amag-titanalr.html on April 20, 2016.