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Title: FAILURE OF THE CHASSIS OF ROLLER SKATESFOR AGONISTIC FIGURE SKATING
Author: Giorgio Olmi
PII: S2213-2902(14)00019-4DOI: http://dx.doi.org/doi:10.1016/j.csefa.2014.08.002Reference: CSEFA 62
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Received date: 30-7-2014Accepted date: 21-8-2014
Please cite this article as: Giorgio Olmi FAILURE OF THE CHASSISOF ROLLER SKATES FOR AGONISTIC FIGURE SKATING (2014),http://dx.doi.org/10.1016/j.csefa.2014.08.002
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FAILURE OF THE CHASSIS OF ROLLER SKATES FOR AGONISTIC FIGURE
SKATING
Giorgio Olmi
Department of Industrial Engineering (DIN), University of Bologna, Bologna, Italy
Corresponding Author:
Prof. Giorgio Olmi, Ph.D.
Department of Industrial Engineering (DIN)
University of Bologna
Viale del Risorgimento, 2 - 40136 BOLOGNA (BO) - ITALY
Phone: +39 051 2093455, +39 051 2090474 (Lab.), +39 0543 374427 (in Forlì)
Fax: +39 051 2093412
E - mail: [email protected]
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Abstract:
The subject of this work was to investigate the early failure, which occurred in the chassis of a roller skate
for figure skating. The paper deals with the preliminary analysis of the crack and with the integrated
approach, which had to be followed to overcome the problem. Literature in the fields of physiology and
biomechanics was studied to correctly simulate the load distribution on the chassis. Finite element
simulation, experimental stress analysis and analytical modeling of impact phenomena had to be combined
together to estimate the entity of dynamic loads and the corresponding state of stress. The analysis led to the
determination of the primary cause of failure, bending fatigue, and to the suggestion of a simple solution to
improve and optimize the project.
Keywords: figure roller skating, impact load, bending fatigue, strain gauge testing, structural optimization
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1. Introduction
Figure roller skating is nowadays a sport being practised by thousands of people at a professional or semi-
professional level. One of the most impressive figures in exhibitions and competitions consists in jumps:
during these evolutions the skater gets elevated up to 400 mm, just after the wheels drop down to the ground
with a strong impact. From the mechanical point of view, the impact has a quite serious outcome, since a
high level of load is transmitted to the skate chassis. Moreover, its entity is quite difficult to estimate, as it is
highly dependent on the skater mass, on the elevation and on the type of figure being performed. A further
important issue stands in the number of jumps that are repeated throughout an exhibition and especially
during the many training hours that every professional skater usually undergoes. The question of mechanical
resistance is made more and more complicated by the increasing demand for lighter structures, due to the
positive outcome on the technical quality of figures during competitions.
This paper deals with the development of the prototype of a novel skate chassis. This is intended to be used
in figure roller skating at a professional agonistic level. Its main feature consists in its lightness, thanks to the
reduced thickness and to the adoption of an aluminium alloy material, P-AlMgSi (6060) – UNI 9006/1,
whereas the previous version had been made of commercial steel. This low weight, corresponding to a mass
of just 144 g, led initially to a very positive outcome in terms of sport performance. However, unfortunately,
a failure occurred after just six months of use by a professional female figure skater. The occurrence of this
failure, which consisted in a crack that nucleated and propagated under bending tensile stress and led to the
early disposal of the prototype, can be regarded as the primary motivation for this paper.
An image of the roller skate and of its chassis is shown in Fig. 1 (a), whereas the cracked component is
depicted in Fig. 1 (b, c). It can be observed that failure occurred at the lower part of the chassis, which
withstands a bending tensile stress due to the skater own weight in static and especially in dynamic
conditions. A Brinell hardness test was performed on the material of the cracked prototype and HB = 33 was
estimated. This value is well corresponding to that of a P-AlMgSi at the annealed state.
The subject of this study was therefore to determine the states of load and, in particular, of stress and strain,
occurring in the chassis in operation conditions, and to retrieve its points of weakness. This was the
preliminary step for the improvement of the project and for the development of a modified version of the
prototype. The main criticalities that had to be overcome can be summarized in the following points:
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A numerical model simulating the state of stress of the chassis can indeed be developed, however,
some difficulties arise (see the following points) that require a careful experimental validation.
The way how the vertical load gets distributed over the chassis is unknown and of not easy estimation.
The entity of load in impact condition is also quite difficult to determine by a theoretical approach
(numerical or analytical tools).
Connections to the boot
(a)
(b)
Connections to the wheels
(c)
Fig. 1: (a) Figure roller skates and detail of the chassis; (b, c) photos of the cracked component
2. Load distribution and finite element model of the chassis
With the aim of overcoming the just mentioned critical issues, a literary review was performed regarding the
physiology and the biomechanics of the lower limb, with particular reference to the mode of load
transmission. Regarding this point, the most widely accepted theory is that by Kapandji [1], according to
which the plantar vault may be compared with an architectural vault supported by three arches. This theory
has been confirmed also by subsequent studies in the biomechanics and medicine fields [2-4]. The vertical
load withstood by the vault acts at three points indicated as A, B and C, which lie at the corners of an
approximately equilateral triangle (Fig. 2 (a)).
The body’s weight is therefore distributed along three directions, towards points A, B and C, which are
usually indicated as “pressure concentration points”. The amounts of load being transmitted to the three
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concentration points, and then to the ground, are proportional to the heel height, which depends on the
geometry of the roller skate boot. Considering the most usual height for professional skates, about 50 mm
(Fig. 2 (b)), the vertical load transmitted by the body gets concentrated mainly at the front zone of the sole,
i.e. at points A and B. Under this hypothesis, the analysis of Refs. [1-4] yields useful information in terms of
the percentage amounts of the loads acting at the three points
The static load due to the athlete’s weight was initially considered: in the present case the total mass was 54
kg, corresponding to a force of about 530 kg. According to [1-4], considering that weight acts on just one leg
during figures, the loads were so estimated: 118 N (22.3% of the total) acting on A, 235 N (44.3%) on B and
177 N (33.3%) on C. These forces acting on concentration points are then transmitted by the foot sole to the
boot and by the boot to the chassis. Figure 2 (c) depicts a plant view of the chassis, with the superposition of
the foot sole and of related concentration points: it is interesting to observe that the line connecting the
forward concentration points (the most loaded: A and B) intersects the chassis at the crack location. The
model was constrained, considering the actual hyperstatic connections between the chassis and the two
couples of carriers.
A
B
C(a)
(b)
(c)
50 mm
Fig. 2: (a) Load distribution according to the vault theory [1]; (b) shape of the boot and heel height; (c)
Concentration points and related locations with respect to the chassis plant
A sketch of the outcome of the finite element model (FEM) of the chassis is shown in Fig. 3 (a): from a
qualitative point of view, it can be emphasized that, considering the load distribution discussed above, the
peak value for stress has been found at the crack initiation point. However, at this stage, it was not possible
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to process the data, as the model needed validation and the impact load still had to be evaluated. It was
anyway an important step, since the model could be used to individuate the optimal location of strain gauges,
to be applied to an identical not cracked prototype, as close as possible to the most loaded area (i.e.: the crack
location).
3. Experimental procedure
Two electrical strain gauges, auto-compensated for aluminium alloy, were bonded at the front zone of the
chassis at both sides, very close to the crack location. The procedure of strain gauge instrumentation and the
state of strain at the bonding location are sketched in Fig. 3 (b, c). Strain gauges were connected to form two
quarter Wheatstone bridges by three-wire connection. The decision of making use of strain gauges is
supported by many papers in literature [5-16], dealing with on fields tests by instrumented components or
specifically developed load cells. Especially in the case of dynamic loads, the execution of tests in the field is
often the only option to get a reliable estimation [6-7, 9, 11, 13, 16].
(a)
(b)
(c)
Fig. 3: (a) Outcome of the FEM model of the chassis; (b) Application of electrical strain gauges; (c) strain
predicted at the gauge location
The experimental campaign was divided into two sessions: in the first one the load consisting in the athlete’s
own weight, was statically applied, with five replications. This session led to a validation of the numerical
model.
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The second session was framed within the training of the professional skater, with the aim of measuring the
impact load. The measuring chain (Fig. 4 (a)) consisted of long cables (5 m) between the strain gauge sensor
and a connector block. The platform output was connected to a DAQ Card, inserted into a laptop slot. A
LabView program was specifically developed to assist the acquisition phases, to record the data and to set
and control the sampling frequency. Regarding this issue, a frequency of 5 kHz seemed to be reasonably
suitable for the full acquisition of the impulsive peak of strain. Dynamic tests were performed, acquiring
analogical signals by the two strain gauge quarter bridges: strains were independently and simultaneously
recorded on two channels. For processing the data, averages between the two acquisitions were then
computed. The athlete was asked to perform a series of jumps with and without run-up and the strains were
consequently acquired. During all the tests the reference elevation from the ground of h = 400 mm was
approximately reached.
4. Experimental results and discussion
The static test led to the determination of an average (among the 5 replications) strain of 55 m/m at the
strain gauge location: this value is the same as that yield by the FEM model at the same zone. This was a
very promising result, regarding the assumptions on load distributions.
The impact tests led to quite repeatable results: one of the outputs of the campaign is shown in the graph in
Fig. 4 (b), where the averaged (between the outputs of the two channels) measured strain is plotted vs. time.
Two results are significant regarding this graph: the entity of the peak, 400 m/m and the duration of the
impact, approximately 0.13 s.
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h = 400 mm
maximum elevation
yAk impact
conditions
(a)
(c)
-100
0
100
200
300
400
0.00 1.00 2.00 3.00 4.00 5.00 6.00
Time [s]
Str
ain
[m
icro
stra
in]
Str
ain
[mic
ron
/m]
(b)
Fig. 4: (a) Experimental testing and related measuring chain; (b) strain plotted vs. time during a jump and
related impact; (c) a sketch of the roller skate: parameters and conditions for the analytical model
Regarding the first issue, comparing the values of 400 m/m (impact) and of 55 m/m (static condition), it
can be argued that the impact leads to an increase of the strain state by an (impact) factor of 7.3 [17]. The
total incremented vertical load was therefore initially roughly estimated, multiplying the static load of 530 N
by the same factor, with the assumption of a perfectly linear relationship. The value of 3.855 N is yield as the
result of this computation.
The following step consisted in a more proper calculation of the impact force by an analytical model. Figure
4 (c) shows a scheme of the impact phase: mA indicates the combination of the masses of the skate and of the
athlete, whereas mB stands for the mass of the ground. The impact force Fi can be estimated [17-18] as in Eq.
(1), where Ay , Ay and yA respectively indicate acceleration, speed and displacement of the skate and of the
whole athlete’s body. The equivalent stiffness, resulting by the combination of those of the boot and of the
chassis is indicated by k.
BA
A
AA
i
mm
m
kyy
tF11
(1)
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With the assumption that the mass of the ground is much greater than that of the skater (mb >> ma), Eq. (1)
may be simplified as in Eq. (2).
AAAi kymytF (2)
Moreover, under the hypothesis that the impact between the skate wheels and the ground is fully elastic, the
impulse Iy along the (impact) vertical direction can be computed as follows, Eq. (3):
Ty
m
kymdty
m
kyTymdtkymydttFI
AAA
T
AA
AAA
T
AAA
T
iy max
000 2020 (3)
According to [18], it can be reasonably supposed that the impact force Fi has a sinusoidal trend, with
equation F(t)=Fmax.sin(t), where =/T and T represents the impact duration. Assuming a linear trend for
the displacement yA, the integral of yAdT over the impact duration can be approximated as ymaxT/2, where
ymax stands for the maximum elongation. Moreover, according to the elastic impact model Ay (T) = - Ay (0).
The peak of the impact force, Fmax (corresponding to ymax) can be then computed, according to [18], as the
product between /2 and the impulse yield by Eq. (3).
Ty
m
kymIF
AAAy max.max 2
0222
(4)
Considering Eq. (4), it can be observed that the second term contains the impact duration T and the
maximum elongation ymax. The equation can be simplified again, observing that these two terms are
reasonably very low. On the other hand, the first term contains three significant terms: the inverse of T, the
mass of the skater, and the speed just before the impact. The conclusion is that the second term can be
neglected with respect to the first one.
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01
022.max AAAA ym
TymF (5)
Considering and elevation of 400 mm, the speed term, evaluated by the well known formula gh2 , is equal
to 2.8 m/s. Introducing the value of T=0.13 s, the impact force is finally evaluated in Eq. (6): it is interesting
to remark that this value is well consistent to the previously roughly estimated, with a discrepancy of 5%.
NT
ymT
F AA 655.38.2541
01
.max (6)
The numerical model was then integrated by the experimental data and used to simulate the distribution of
stress under the impact. The maximum value for von Mises equivalent stress was retrieved at the crack
location (Fig. 5 (a)). In particular the estimated value was around 65 MPa, which is not particularly high, but
can be consistent with the fatigue failure of a component in P-AlMgSi alloy.
Considering that an average number of 4 leaps per min is usually performed during training and that the
training sessions for a professional athlete take place every day (6 days per week) for at least four hours, a
total of over 200,000 jumps (i.e. fatigue cycles) can be reasonably expected in a six-month time.
As mentioned in the Introduction, HB = 33 was retrieved on the cracked component. This outcome makes it
possible to estimate a ultimate strength (u) around 100 MPa. Even though aluminum alloys do not have a
true fatigue limit, a common practice is to take the fatigue strength at 5108 cycles as the pseudo fatigue limit
value [19]. According to [19-20], the bending fatigue limit (f) of these alloys is 0.4 times the ultimate
tensile strength: around 40 MPa, being lower than 65 MPa. A difficult point stands in the estimation of the
aluminium alloy response in the finite life field. However, following the approach for steels [19], it is
possible to estimate an approximated S-N curve, which is interpolated between 0.9u at 1,000 cycles and f
at 5108 loops. This curve is plotted in Fig. 5(b) in the bi-logarithmic scale: despite the rough approximation,
it is interesting to notice that the expected life for a stress level of 65 MPa is around 300,000 cycles, a
duration being of the same magnitude of order as the observed one.
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10
100
1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
Str
ess
[MP
a]
Cycles
65 MPa
u9.0
f
New holes
65 MPa
(a)
(b)
(c)
Fig. 5: (a) State of stress of the chassis with peak value at the cracked location, (b) approximated S-N curve
of P-AlMgSi in the finite life domain; (c) improved and optimized project
Finally, the validated model made it possible to improve the project: the thickness at the cracked location
was increased to reduce stress under the bending fatigue limit. On the other hand, holes were added at the
central and real sides of the chassis, in order not to increase the mass of 144 g (Fig. (5 (c)). As it is visible in
Fig. 3 (a) and 5 (a), this area exhibits very low values of stress, a possible reason standing in the occurrence
that it is located under the vault between the three concentration points.
5. Conclusions
This paper dealt with the analysis of a novel chassis for figure roller skates, made of P-AlMgSi alloy, which
experienced a premature failure. An integrated approach had to be used to overcome the several criticalities
of the study. In particular, a careful literature review was necessary to get a reliable estimation of the load
distribution of the chassis, according to the vault theory. A finite element model of the chassis was necessary
to determine the stats of stress and strain in the structure. Experimental stress analysis was used to calibrate
the model and to study dynamic conditions: the results were also integrated into an analytical model to study
the impact of skate wheels to the ground. The research led to the individuation of the primary cause of
failure, standing in bending fatigue, due to the high number of jumps (i.e.: fatigue cycles) being performed
during figure skating training. A solution to the problem was suggested, which led to an improved and
optimized project of the chassis with positive outcomes (from the technical and mechanical points of view)
in its use.
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Acknowledgements
The author would like to gratefully acknowledge Prof. Alessandro Freddi of the University of Bologna for
his support in the interpretation of the experimental data.
References
[1] A.I. Kapandji, The Physiology of the Joints: Lower Limb (Volume 2) (5th Edition), Churchill
Livingstone, 1988.
[2] P.R. Cavanagh, M. M. Rodgers, A. liboshi, Pressure Distribution under Symptom-Free Feet during
Barefoot Standing, Foot & Ankle International, 7(5) (1987) 262–278.
[3] D. Daentzer, N. Wülker, U. Zimmermann, Observations concerning the transverse metatarsal arch, Foot
and Ankle Surgery, 3 (1997) 15–20.
[4] K.-J. Chia, D. Schmitt, Mechanical energy and effective foot mass during impact loading of walking and
running, Journal of Biomechanics, 38 (2005) 1387–1395.
[5] G. Olmi, A. Freddi, Crack initiation and propagation in a press column under compressive load, The
Archive of Mechanical Engineering, 52(4) (2005) 324–340.
[6] N. Petrone, Acquisition and analysis of ground reaction forces and foot orientation of in-line skates
during track speed skating, In: XXI Congress, International Society of Biomechanics. Journal of
Biomechanics, pp. 398, Elsevier, Taipei (2007).
[7] G. Olmi, A. Freddi, D. Croccolo, In-Field Measurement of Forces and Deformations at the Rear end of a
Motorcycle and Structural Optimisation: Experimental-Numerical Approach Aimed at Structural
Optimisation, Strain, 44 (2008) 453–461.
[8] G. Olmi, Investigation on the influence of temperature variation on the response of miniaturised
piezoresistive sensors, Strain, 45 (2009) 63–76.
[9] G. Pellicioli, N. Petrone, Experimental Strain Analysis of the Mast of a 420 Sailboat During Sailing,
Strain, 46 (2010) 482–492.
[10] G. Olmi, A new loading-constraining device for mechanical testing with misalignment auto-
compensation, Exp. Techniques, 35(6) (2011) 61–70.
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[11] N. Petrone, Field acquisition of ski boots flexural behaviour for the correct definition of standard
laboratory tests, In: 19th International Conference on Ski Trauma and Safety. Keystone, Colorado
(2011).
[12] G. Olmi, A Novel Method for Strain Controlled Tests, Exp. Mech., 52(4) (2012) 379–393.
[13] D. Croccolo, M. De Agostinis, G. Olmi, A. Tizzanini, Analysis of the Stress State in Brake Caliper
Mounts of Front Motorbike Suspensions, Adv. Mech. Eng., (2013) Article number 525010.
[14] D. Croccolo, M. De Agostinis, P. Mauri, G. Olmi, Influence of the engagement ratio on the joint
strength of press fitted and adhesively bonded specimens, International Journal of Adhesion and
Adhesives, 53 (2014) 80–88.
[15] D. Croccolo, M. De Agostinis, P. Mauri, G. Olmi, Effect of the Engagement Ratio on the Shear
Strength and Decoupling Resistance of Hybrid Joints. In: Adhesives: Mechanical Properties,
Technologies and Economic Importance, Nova Publisher, 2014.
[16] G. Olmi, An experimental investigation on a crack propagating from a geartrain housing in an
asphalt milling machine, Engineering Failure Analysis, 38 (2014) 38–48.
[17] R.C. Juvinall, K.M. Marshek, Fundamentals of Machine Component Design (4th Edition), Wiley &
Sons ltd, 2005.
[18] W.J. Stronge, Impact Mechanics, Cambridge University Press, Cambridge, 2000.
[19] Y.-L. Lee, J. Pan, R. B. Hathaway, M. E. Barkey, Fatigue Testing and Analysis (Theory and
Practice), Elsevier Butterworth–Heinemann, Burlington, USA, 2005.
[20] G. Niemann, H. Winter, Maschinen – Elemente, Band. 1, Sprinter-Verlag Berlin, Heidelberg, 1981.
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Figure Captions
Fig. 1: (a) Figure roller skates and detail of the chassis; (b) a photo of the cracked component
Fig. 2: (a) Load distribution according to the vault theory [1]; (b) shape of the boot and heel height; (c)
Concentration points and related locations with respect to the chassis plant
Fig. 3: (a) Outcome of the FEM model of the chassis; (b) Application of electrical strain gauges; (c) strain
predicted at the gauge location
Fig. 4: (a) Experimental testing and related measuring chain; (b) strain plotted vs. time during a jump and
related impact; (c) a sketch of the roller skate: parameters and conditions for the analytical model
Fig. 5: (a) State of stress of the chassis with peak value at the cracked location, (b) approximated S-N curve
of P-AlMgSi in the finite life domain; (c) improved and optimized project
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FAILURE OF THE CHASSIS OF ROLLER SKATES FOR AGONISTIC FIGURE
SKATING
Giorgio Olmi
Highlights:
A high impact load is transmitted to the chassis during figure skating jumps.
The largest amount of load acts at the forward part of the chassis.
Strain gauge in-field tests were used to estimate the impact loads.
Fatigue failure is due to the high number of jumps performed in training sessions.
The project underwent structural optimization without weight increment.
