Analysis of the Suspension Design Evolution in Solar Cars

Felipe Vannucchi de Camargo
Research Fellow
Dept. of Advanced Mechanics and Materials
Alma Mater Studiorum University of Bologna
Italy
Cristiano Fragassa
Assistant Professor
Department of Industrial Engineering
Alma Mater Studiorum University of Bologna
Italy
Ana Pavlovic
Adjunct Professor
Dept. of Advanced Mechanics and Materials
Alma Mater Studiorum University of Bologna
Italy
Matteo Martignani
Mechanical Designer
Onda Solare Association
Italy
Analysis of the Suspension Design
Evolution in Solar Cars
The contrast between modern mobility alternatives and the seek for
sustainability has been an essential concern for industry in the last
decades, boosted by technologies that have been progressively narrowing
this gap. Among them, solar cars represent a contemporary trend to supply
this need. Given the complexity embraced by this technology, the
attainment of an efficient design demands the improvement of every aspect
of the vehicle, including its mechanics. Performing a critical role on the
vehicle’s stability, the suspension system of solar cars is thoroughly
investigated in this work, in particular the evolution of the structural part
directly responsible for undertaking the forces subjected to the wheel hub.
Three different shapes made out of carbon fiber reinforced plastic are
analysed and compared through static and modal finite element analysis:
two front forks meant to be coupled to a wishbone joint, and a wheel hub
connected to a novel sliding hub system.
Keywords: Solar vehicles, Suspension, Sliding hub, Carbon fiber, FEM
Static Analysis, Modal Analysis.
1.
INTRODUCTION
The main principle promoted by solar vehicles is the
possibility to generate energy without harming the
environment. However, the constant task of a car to
overcoming the inertia provided by surrounding
resistances to move makes most of the energy generated
by the vehicle to be dissipated through vibrations and
motions [1,2]. Hence, the challenge to avoid energy loss
is of paramount importance and attaining this premise
might be a quite complex engineering endeavour.
To fulfil this goal, all parts of an efficient vehicle
must be designed to be as lightweight and resistant as
possible [3], while a harmony between their relative
movements should be kept to attenuate friction, which is
nothing but energy loss sustained by a higher demand
on the battery.
The suspension is a vital system of any car for
offering stability, safety, vibrations absorption and
softening mechanical efforts on other components
extending their operational life; hence, enhancing the
suspension efficiency is a compelling need if one
desires to achieve an efficient vehicle design, especially
in solar vehicles where energy management is a
particularly important issue [4,5].
Three different wheel support systems, designed by
Onda Solare Italian designers to meet the technical
requirements of three diverse categories of solar cars,
are here analysed. The main scope is to characterize
their static and dynamic behaviour when mechanically
demanded, providing a scientific-based definition on
which is the most advantageous design.
Received: October 2016, Accepted: November 2016
Correspondence to: Felipe Vannucchi de Camargo
CIRI Advanced Mechanics and Materials
Alma Mater Studiorum University of Bologna, Italy
E-mail: felipe.vannucchi@unibo.it
doi:10.5937/fmet1703394V
© Faculty of Mechanical Engineering, Belgrade. All rights reserved
1.1 Solar Car
The solar car concept arose in 1955 with William Coob
from General Motors with his exhibition of the
“Sunmobile” car in Chicago, introducing the possibility
of using photovoltaic cells to convert sun rays into
electricity for a car in a time where a diesel-fuelled
empire ran the automotive industry supported by
powerful oil companies. Even though the non-renewable
fuel dependence is still a reality nowadays, the electric
vehicles trend has begun to hold its market share powered
by the mass-produced pioneer Toyota Prius and more
recent alternatives such as the acclaimed Tesla S.
Addressing to foment the progress on solar car
technologies, several solar races are held frequently in
countries such as Australia, United Arab Emirates, Chile,
Belgium and South Africa; encouraging renowned univer–
sities and research centres worldwide to prepare for these
competitive races while developing novel technologies,
promoting popularity, and intensifying industrial attention
on this eco-friendly automotive segment.
Given the ongoing perspective and reassuring that
this work is up to date, one can highlight that the current
champion of the Cruiser category at the most aggressive
solar car race, the World Solar Challenge, is studying in
the last years how to continually improve the
suspension design of their car [6].
Each wheel support was applied on one of the three
solar cars considered for this work, all corresponding to
a diverse World Solar Challenge (WSC) racing
category: Adventure, Challenger and Cruiser (Figure 1),
considering 80 kg passengers. Their main differences
are displayed in Table 1.
The categories in which each vehicle belongs have
some particular characteristics:
• Adventure: is a non-competitive category,
aiming at inspiring talented students and
engineers to abet the solar vehicles concept;
FME Transactions (2017) 45, 394-404 394
Figure 1. Solar cars investigated from categories: Adventure (a), Challenger (b) and Cruiser (c)
• Challenger: is the most competitive category and
behold the fastest cars with enhanced designs
and finest materials on a single stage drive
course;
• Cruiser: is also a competitive and new category,
based on a regularity trial, aiming at
developing novel concepts of transportation
and energy efficiency for the next generations
of solar cars, encouraging this market segment.
1.2 Suspension
The suspension is certainly one of the most vital
systems for the proper car functioning. It is not only
responsible for absorbing external vibrations providing
comfort to the passengers, but also for shock softening,
protecting all the mechanical parts while sustains the
entire vehicle weight, maintaining the tires in firm
contact with the road enhancing propulsion and safety.
Suspensions can be generally divided into two main
groups [7]: dependent and independent. The dependent
suspensions have both right and left wheels connected
by a transversal trailing rod, so when one of the wheels
suffers a vertical displacement (e.g. due to a bump), the
other wheel is also affected. On the other hand, the
independent suspensions allow vertically autonomous
movements for each wheel. The main advantages of the
dependent system are low cost and low maintenance
while occupying less space; while the independent
system leverages are improved steering, handling and
comfort.
In solar racing vehicles, there are some preferred
suspension designs available. Among them, for offering
enhanced steering precision and keeping an adequate
camber angle in curves, wishbone connections are
widely disseminated either in all wheels of a fourwheeled car, or in the front wheels of a three-wheeled
car, which generally considers a trailing arm suspension
for the rear wheel. Rear trailing arm suspensions are
adopted for conserving energy on bumpy roads once it
allows only vertical movements; for offering improved
lateral load handling capacity; and diminished bending
stresses on suspension components [8].
Still speaking of independent systems, MacPherson
is also a common design choice for having a cheap and
light design [9], even though its load carrying capacity
is relatively low. Both MacPherson [10] and wishbone
suspensions [6,11,12] are reported to be used in solar
racing cars before. Given the current overview, aside
from the wishbone’s wheel support evaluation in this
study, the analyse of the sliding hub is then particularly
relevant due to its innovative feature.
The aforementioned structures are applied in various
competitive solar vehicles nowadays, such as the
vehicles from the University of Eindhoven, featuring
rear trailing arms [6] (Figure 2); the University of New
South Wales, with front double wishbones [13] (Figure
3); the University of Johannesburg, with double
wishbone suspension composed by composite upright
and A-arms [11] (Figure 4); and Stanford with a double
wishbone multi-link composition (Figure 5).
The choice for a transversal leaf spring suspension
derives from a few important facts for building a
competitive solar car: it reduces considerably the
unsprung weight; it contributes with less overal weight
to the suspension system (considering also the fact that
all suspension components for the Cruiser vehicle are
made of carbon fiber); and lowering the center of
gravity upgrading the stability of the car. Furthermore,
similary, non-transversal composite leag springs have
already been used in a solar racing car representing
good performance and meeting all design requirements
[14].
Table 1. Characteristics of the solar cars analysed
Category
Adventure
Challenger
Cruiser
Weight [kg]
260
200
280
Passengers
1
1
4
Total Weight [kg]
340
280
600
Wheels
3
4
4
Approximate dimensions [m]
5.00 x 1.80 x 1.25
4.50 x 1.80 x 1.25
4.65 x 1.80 x 1.30
Cruising Speed [km/h]
51
61
65
Maximum Speed [km/h]
100
120
100
Suspension
Double wishbone (front) and
trailing arm (rear)
Double wishbone
Sliding hub
395 ▪ VOL. 45, No 3, 2017
FME Transactions
Figure 2. Rear trailing arm suspension by Solar Team
Eindhoven [6]
Figure 3. Front double wishbone suspension by Sunswift
[13]
Challenger and Cruiser cars, respectively; and these
geometries are henceforth quoted as A, B and C. The
most noticeable difference among these supports,
besides the compact size of geometry C, is that each one
offers a particular main degree of freedom for absorbing
the impact subjected to the vehicle by its own motion:
• Geometry A: Offers a translational displacement
normal to the road surface, connected by two
ball joints inherent to the wishbone design;
• Geometry B: Also linked by two ball joints,
presents, as prominent degree of freedom for
undertaking the vertical efforts of the car, a
rotation axial to the transversal axis of the
vehicle, with a 10o range;
• Geometry C: Similarly to geometry A, offers a
translation to support vertical efforts, although a
fixed sliding hub guides it.
As long as every relative movement provided by a
mechanical joint involves a certain friction to happen, it
is important to underline that this energy spent by a
joint, in an electric car, is prevenient from the battery.
Thus, the friction involved on every inter-part
connection must be decreased to the minimum possible
level in order to enhance the energy efficiency.
The novel design of the non-wishbone wheel
support studied presents a layout composed by a wheel
hub connected to a sliding hub, which is linked directly
to the spring, aiming to decrease the energy spent due to
friction. It is known that a single ball joint requires less
friction than a sliding hub, but the numerous joints that
a wishbone design exhibits as a whole makes the
alternative of a single sliding surface to become
interesting. Besides, this design is more compact and
requires a smaller number of parts, also offering weight
reduction.
Figure 4. Double wishbone suspension by UJ Solar Car [11]
Figure 6. Wheel support geometries for the conventional
categories of (a) adventure; (b) challenger; (c) cruiser
Figure 5. Double wishbone multi-link suspension by the
Stanford Solar Car Project
2.
MATERIALS AND METHODS
2.1 Wheel Support Designs
In this work, three different designs are considered and
compared: two forks that are meant to be coupled with a
double wishbone (Figure 6a,b), although their shape and
assembly layout is quite distinct, and a new and
uncommon wheel hub solution (Figure 6c), all of them
connected to a transversal leaf spring. The mounted
hubs are shown in Figure 7.
The volumes of the wheel supports are 1340.20 cm3,
1464.10 cm3 and 257.35 cm3 for the Adventure,
396 ▪ VOL. 45, No 3, 2017
Figure 7. Mounted wheel supports for the conventional
categories of (a) adventure; (b) challenger; (c) cruiser
2.2 Carbon Fiber
According to the 21st century demand for novel
technologies and products [15] and the aforementioned
FME Transactions
current and continuous seek for lightweight resistant
materials, fibers and composites are undoubtedly a
strong alternative for supplying this demand with
successful performance on acute applications [16-19].
In turn, with respect to Carbon Fiber Reinforced
Polymers (CFRP) specifically, the application on
automotive field is thoroughly consolidated since the
Formula 1 pioneering success in 1981, proposing a
carbon fiber composite monocoque chassis [20].
Nowadays, in order to enhance resistance, reduce
weight, or both, the usage of this composite in basic and
structural parts for race cars as well as wholesale
vehicles is typical.
The energy efficiency achieved by using such
material is especially appealing to solar vehicles
[21,22], once their energy source and current conversion
technologies require the most efficient solar arrays,
batteries, design and materials for achieving a good
overall performance. Therefore, once a car with reduced
weight would demand less energy to surpass inertia, it is
encouraged to widen the usage of composites on
structural parts, such as previously implemented
suspension components [11].
Apart from the mechanical characteristics, the
utilization of carbon fiber is also supported by its
recycling possibility [23], once eco-friendly alternatives
have been increasingly studied on the composites field
[24] due to their large-scale usage and consequent
significant environmental impact. Moreover, its safety
properties such as gas barrier and flame retardant [25]
make the material yet more worthwhile, providing
security to vehicles; aspect that might be neglected in
some cases despite being of utmost importance [26].
The two forks from geometries A and B and the
wheel hub from geometry C were manufactured with
pre-impregnated carbon fiber sheets on a temperatureand-humidity-controlled room, followed by an
autoclave curing process. As an example, a picture of
the manufactured geometry A is shown in Figure 8:
Figure 8. Adventure vehicle’s wheel support in carbon fiber
Carbon fiber composites are certainly disseminated
by solar car teams throughout the world, mainly based
within an epoxy resin matrix, having already provided a
weight saving of 55 kg in some vehicles [27].
Furthermore, its application, specifically on a suspension
system, does not provide only weight reduction but also
increase the safety factor of its components [11].
Actually, the emphasized weight optimization
importance for obtaining a good energy efficiency [3]
can be quantified: stating as reference a 10% weight
reduction, the generated fuel saving for a regular
commercial car ranges from 6-8%; the fuel economy on
a hybrid vehicle can reach up to 5.1%; and the electric
range on an electric car can be improved by 13.7% [28].
Furthermore, a similar study about the weight
optimization of suspension knuckle for a solar race car
has already been performed [29], and, for this specific
case, it was found out that a 452 g weight reduction in
the car represents an energy saving as high as 18.6 Wh.
For this work, the composite material considered has
an epoxy matrix and a unidirectional T800 carbon fiber
reinforcement, by Toray; in which pre-impregnated 0.25
mm thick plies assembled under a [90/03/+45/45/03/90]s orientation result in a variable thickness part
(for geometries A and B) and a 5 mm thick part (for C).
This configuration is adequate to the effort the wheel
hub is subjected, with the longitudinal 0° fibers holding
the biggest load share, while the ±45° plies contribute to
torsional stiffness and the 90° plies grant a good
mechanical resistance in all main directions making a
quasi-isotropic material. A fiber volume of 60% was
adopted and the composite is considered homogeneous.
The density was calculated with the average value of
1.54 g/cm3, while orthotropic mechanical characteristics
and stress limits [30,31] are described in Table 2 for this
specific laminate.
In order to point out the reason why carbon fiber is
the selected material, the simulations carried in this
work were also performed considering aluminium 6151T6, a common material choice when low cost and light
weight are expected, and carbon steel AISI 1040 hot
rolled, already used for building wishbone suspension
components in other racing car categories [32,33]. Some
main properties of aluminium and steel are respectively:
Young Modulus of 71 GPa and 200 GPa; Poisson ratio
of 0.33 and 0.29; Shear Modulus of 26.7 GPa and 77.5
GPa; and density of 2.77 g/cm3 and 7.80 g/cm3 [34,35].
The finite element method (FEM) based analyses of
a fiber reinforced composite might be performed by two
general approaches [36]: the micromechanical, where it
is modeled as a multi-phase composition; and the
macromechanical, where the part is treated as an
equivalent homogeneous material. Therefore, as this
work is based on a preliminary study concerning the
global behaviour of the component, the macromechanical approach is adopted, which considers a
homogeneous anisotropic material. Other researches
have already been carried with this same assumption
[37,38], specifically for a composite reinforced by a preimpregnated unidirectional fiber by Toray [36], just like
the present work. The adoption of the macro-mechanical
premise is actually advised for composite materials
which are not solicitated beyond the elastic regime,
once until the failure of the first layer, the assemble can
be seen as a homogeneous part [30].
Finite element analyses were performed in terms of
static and modal studies.
Table 2. Elastic modulus (E) and Shear Modulus (G) [GPa], Poisson ratio, and stress limitis [MPa] for the CFRP laminate
E1
112.5
E2
49
E3
9
FME Transactions
ν12
0.2
ν23
0.25
ν13
0.25
G12
13
G23
3.4
G13
3.4
σ1,rupture
1133
σ2,rupture
467.5
σ3,rupture
66
τ12
241
τ12
100
τ12
100
VOL. 45, No 3, 2017 ▪ 397
2.3 FEM Static Simulation
The simulations carried to assess the mechanical
response of all parts were static once this assumption is
proved to grant results faithful to the actual part
behaviour [39] and has been widely developed in
similar studies [6,31,40,41,].
As for the boundary conditions, given that each
wheel hub was applied to a different vehicle with own
dimensions and design, the constraints are singular in
each case. In all simulations, a force correspondent to
the weight of the full car (including 80 kg passengers)
divided by the number of wheels under a 3G
acceleration was assumed. Also, this acceleration was
already set as constraint for vertical forces in an
analogous suspension study [42].
While for geometries A and B a frictionless support
on the wishbone connection was assumed, a fixed face
condition was imposed for geometry C. Besides, a fixed
displacement on the axial direction to the wheel was set
up for A and B once no movement is allowed in this
direction due to the wheel attachment. The boundary
conditions are shown in detail in Figure 9. The
simulations concern a straight drive condition.
Considering the weight of the car with passengers
(Wt) and dividing it by three or four to define the
weight applied on each wheel (Ww), the resulting mass
was multiplied by the pre defined 3G acceleration. An
approximate force (Fw) used in the simulations is stated
for each wheel hub as showed in Table 3.
The mesh data is displayed in Table 4, and the
meshed geometries are shown in Figure 10.
Table 3. Weight and forces definition
A
B
C
Wt [kg]
340
280
600
Ww [kg]
114
70
150
Fw [kN]
3.3
2.0
4.4
Table 4. Mesh data
A
B
C
Nodes
294 025
306 424
114 863
Elements
81 216
78 443
116 353
3
3
2
0.749
0.787
0.977
Element Size [mm]
Average Quality
Figure 9. Boundary conditions
The three meshes were discretized by a hex dominant
method with 3 mm elements for geometries A and B and
2 mm for C once this support is considerably smaller than
398 ▪ VOL. 45, No 3, 2017
the others. Also, after preliminary simulations it was
noticed that the maximum stress region on geometry C is
the fillet. Therefore, a mesh refinement assumption for
critical fillet sessions [43] was applied on the fillet and its
adjacent faces, based on a size decreasing of the elements
in this area aiming to improve simulation accuracy
assuming 0.2 mm elements.
Figure 10. Mesh application
2.4 FEM Modal Analysis
Modal analysis permits to determine the vibration
response of a structure in terms of natural frequencies
and mode shapes. It is a fundamental step, generally
used as starting point for other more detailed dynamic
analyses (such as harmonic, dynamic and rigid body
motion). It considers that every structure can be
subjected to the influence of variable external forces,
which in case of their variance in a resonance condition
might entail significant wear and durability issues on its
mechanical components [44].
Therefore, modal analysis allows the investigation
of the dynamic properties of structures subjected to
excitation caused by vibrations, aiming to define the
resonant frequencies in a way to foresee and avoid the
resonance phenomenon by improving the given
machine design. This kind of frequency is an outcome
caused by the mutual annulment of the stiffness and
inertial forces; thus, the source governing the vibration
amplitude is damping alone.
For all the endless number of natural frequencies of
vibration existent (each one representing a different
mode of vibration), the part analysed will suffer a
particular deformation, majorly caused either by torsion,
or bending, or compression, and so on so forth.
Considering the wheel supports investigated and the
motion of the car, there are, generally, four types of
static load that can be separately or jointly applied to the
wheels [45]:
• Lateral Bending: when the vehicle steers a corner
in high speed;
• Horizontal Lozenging: due to forward and
backward forces applied at diagonally opposite
wheels;
• Longitudinal
Torsion:
Due
to
bumps
simultaneously acting on two diagonally
opposite wheels, imposing to the structure a
torsion-spring-like solicitation;
• Vertical Bending: basically caused by the car
weight from supporting its weight.
Since this work is based on a static analyse
representing the mechanical demand on the wheel
supports caused by a linear and bumpless motion of the
FME Transactions
vehicle, the concern of the modal analysis is to identify
the lowest modes of vibration in which the frequencies
are able to impose a vertical bending condition to the
parts studied.
3.
RESULTS AND DISCUSSION
3.1 Static Analysis
The FE static analysis permitted to investigate the stress
distributions in respect to the suspensions’ wheel
supports studied (used for Adventure, Challenger and
Cruiser categories) considering different materials
(CFRP, aluminium and steel). Maximum stress regions
are common in all materials and are shown in Figure 11.
As for geometry B, a symmetric well-balanced stress
gradient is evidenced, with critical region located,
naturally, on the wishbone joint. Geometry C shows an
accurately symmetric pattern, with severe stress
clustering on the fillet.
The Von Mises maximum stress results for both
aluminium and steel were exactly the same for each
particular support geometry, explained by the fact
that the isotropic materials are under the same force
and neither reaches the plastic regime. On the other
hand, as long as composites are elastic up to their
rupture, they do not yield by local plastic
deformation such as classical metallic materials.
Hence, the elastic limit corresponds to the rupture
limit and the safety factor is calculated through the
Hill-Tsai method [30].
This criterion states that if its constant (α2) attends
to the condition [0 < α2 < 1], the design is safe. For
geometries A and B, the 3D Hill-Tsai formula (1) was
used since the structures can be considered as solid and
were modeled with solid elements. Instead, geometry C,
modeled as a shell structure for having a constant
thickness and being hollow, has its safety factor
calculated by the 2D Hill-Tsai equation (2), which
considers only in-plane stresses. For the sake of
comparison with the metallic materials, the safety factor
of CRFP supports can be calculated according to the
expression (3) [30].
2
2
2
 σ1   σ 2
  σ3

α =
 +
 +
 −
 σ1,rupture   σ 2,rupture   σ 3,rupture 

 
 

2


1
1
1

 σ1σ 2 −
+
−
 σ 21,rupture σ 22,rupture σ 23,rupture 




1
1
1

 σ 2σ 3 −
+
−
 σ 22,rupture σ 23,rupture σ 21,rupture 


(1)


1
1
1

 σ1σ 3 +
+
−
 σ 23,rupture σ 21,rupture σ 22,rupture 


2
2
 τ12
  τ 23
  τ13


 +
 +

 τ12,rupture   τ 23,rupture   τ13,rupture 

 
 

 σ1
α =
 σ1,rupture

2
Figure 11. Stress concentrations for the categories of (A)
Adventure, (B) Challenger and (C) Cruiser
The maximum stress region on geometry A is the
wheel rod attachment hole. Its small dimensions when
compared to the whole part coupled with the hole’s
inherent stress concentration are responsible for this
outcome. A similar motorcycle fork-shaped moving arm
geometry subjected to its operational efforts has shown
to present exactly the same intensified stressed region,
validating the result [41].
FME Transactions
 σ .σ
1 2
−
 σ 21,rupture

2
  σ2
 +
 
  σ 2,rupture
  τ
12
+
  τ12,rupture

SF =
1




2
−1
2
2

 −


(2)
(3)
α
Finally, Table 5 covers the maximum stress results
and safety factors (SF) of all wheel supports. For the
metals, safety factor is calculated by the ratio of the
Yield Strenght (280 MPa for aluminium and 350 MPa
for steel) and the maximum Von Mises stress.
VOL. 45, No 3, 2017 ▪ 399
Table 5. Maximum Von Mises stress [MPa] for aluminium or steel, maximum principal stresses for CFRP, and safety factors
Aluminium and Steel
CFRP
Von Mises
Maximum Stress
SF
Aluminum
SF
Steel
σ1
σ2
σ3
Adventurer
17
14.7
20.6
15
10
5.2
7
Challenger
15
16.7
23.3
36
18
5.5
4.6
Cruiser
132
1.9
2.6
160
138
-
85
-
τ12
τ13
α2
SF
CFRP
2.7
3
0.013
7.7
4.4
4.4
0.092
2.3
-
0.214
1.2
τ23
3.2 Modal Analysis
The FE modal analysis allowed the investigation of the
dynamic response of the three studied wheel supports.
Given the extremely high frequencies encoutered, the
analysis is limited to the three first resonant frequencies
for each design and material investigated, as displayed
in Table 6.
Table 6. Lowest natural frequencies (in Hz) of Adventure
(A), Challenger (B) and Cruiser (C) wheel supports as a
function of the vibration mode (N)
CFRP
N
1st
2nd
3rd
A
70
471
554
B
144
312
421
C
675
733
1669
N
1st
2nd
3rd
A
64
430
507
Aluminium
B
132
286
384
C
618
672
1528
N
1st
2nd
3rd
A
65
435
507
Steel
B
133
286
387
C
617
671
1529
Table 6 shows that the metallic materials present a
very similar behaviour. Figure 13 illustrates this akin
resonant trend along the subsequent modes of vibration
with the metals curves overlapped and indistinct. Also,
it highlights that carbon fiber parts always present
higher resonant frequencies for the same vibration mode
in a same wheel support design, being therefore a safer
material.
In addition, the first resonant frequencies of the
suspension part of the Cruiser vehicle are the highest,
followed by the Challenger and the Adventure. Thus,
the higher the resonance frequency, the more difficult it
is to be achieved, and the safer the design. Hence, the
analysis is narrowed to carbon fiber, so forth the safest
and most lightweight option.
Besides the frequency magnitude, the load type
described by each vibration mode is an important matter
of concern. For a proper understanding, three axis
should be assumed: transversal and longitudinal to the
vehicle, and normal to the ground. Table 7 reports all
load conditions characterized by the application of a
moment in one of the axis in each vibration mode.
Figure 12 exhibits the expected not scaled deformations
shapes in all cases considering carbon fiber composite
as material only.
400 ▪ VOL. 45, No 3, 2017
Figure 12. Maximum deformation in first three modes of
vibration on (A) Adventure; (B) Challenger; and (C) Cruiser
Table 7. First three modes of vibration and equivalent loads
fI [Hz]
Load1
fII [Hz]
Load2
fIII [Hz]
Load3
A
70
Normal
moment
471
Transversal
moment
554
Longitudinal
moment
B
144
Normal
moment
312
Transversal
moment
420
Normal
moment
C
674
Longitudinal
moment
733
Transversal
moment
1669
Normal
moment
Figure 13. Resonant frequencies for the first three modes
of vibration for metals (full line) and CFRP (dash line)
FME Transactions
However, as previously stated, the most relevant
load type in this study is vertical bending only [45],
which is represented by a moment on the transversal
axis of the vehicle (Figure 14). Thus, the most relevant
results can be narrowed to the lowest vibration mode in
which such effort is present (coincidently, all 2nd
modes), as displayed in Table 7. Figure 15 shows their
respective modal deformation gradient.
Figure 14. Vertical bending condition [45]
Figure 15. Effect of vertical bending deformation (2nd mode
of vibration) on the different suspensions: (A) Adventure;
(B) Challenger; and (C) Cruiser
3.3. Weight Comparison
Besides the mechanical response, the weight of the
supports is a crucial matter of concern, as explained in
previous sessions. Table 8 provides a comparison
among all geometries and materials studied.
Table 8. Wheel hub masses
CFRP
Aluminium
Steel
A
2.1
3.7
10.5
FME Transactions
Mass of each support [kg]
B
2.2
4
11.5
C
0.4
0.7
2
4.
CONCLUSION
Given the current mechanical solicitations, all
geometries seem to withstand their operational forces
well, hence, failure is not a matter of concern. Also, all
designs have high and unattainable resonant
frequencies. For example, a racing car equipped with an
eight-cylinder internal combustion engine of
approximately 750 hp, reaching up to 380 km/h, and all
its inherent vibrations, has as parameter the operational
frequencies ranging from 0.5 Hz to 20 Hz to grant a
trustworthy modal analysis [46]. Thus, the frequency
generated by an extremely light electric solar vehicle
that achieves up to 120 km/h, is undoubtedly in a safer
range of operation.
As for the different geometries, the wheel hubs from
the Adventure and Challenger vehicles demonstrated to
be safer than the Cruiser in terms of stress concentration
and magnitude at operational conditions, although, due
to its reduced dimension, the Cruiser support present
much higher resonant frequencies being safer in this
aspect. Also, the modal results for Adventure and
Challenger are validated, since suspension fork
structures are known for having their legs as critically
affected regions due to bending [47].
On the other hand, regarding the materials,
aluminium and steel have static safety factor
considerably higher than CRFP, independent of the
geometry. However, the modal behaviour of the
structures seemed fairly levelled for all materials, being
preferably dependent on the part geometry.
From an overall perspective, the suspension parts
from the Adventure and Challenger vehicles have
showed to be always safer in both analyses made,
independently from other factors; while the Cruiser hub
is also safe, but significantly less. It is important to
emphasize that this difference comes with a cost, and it
is caused by a noticeable contrast in weight and
dimensions, in which the Cruiser geometry is much
more advantageous than others. Also, it is submitted to
a considerably higher static load.
Therefore, carbon fiber is undoubtedly the best
material for all designs once the resistance is kept at a
high level and the weight of the part is significantly
decreased, as shown by Table 8. The Cruiser’s hub
design is also advised as it is the best in terms of energy
saving due to its lightweight and low operational
friction. Nevertheless, the safety factor presented is seen
as safe but insufficient, so a thickness increase made by
adding a few carbon fiber plies must be considered
aiming to strengthen the part.
The biggest disadvantage of geometry C is that it is
designed focusing on a straight wheel drive, not having
a steering mechanism as good as A and B’s independent
wishbone suspension. For the studied solar car project
this is not a huge issue because the races in which these
vehicles participate, such as in Australia, United States,
Chile and Morocco, are predominantly straight.
However it is meaningful to emphasize that it would not
be the most appropriate design for races held in circuits,
such as Suzuka, in Japan.
As long as this work considers solely the effect
caused on the suspension by the weight of the car with
VOL. 45, No 3, 2017 ▪ 401
passengers on a straight drive assuming a rough road
surface; it is encouraged to perform the analysis taking
into account more extreme boundary conditions such as
turning, in which a force radial to the curve would take
place on the part; and emergency breaking, where the
inertia of the car movement would turn into an
aggravating state of stress on the suspension [47]. Also,
the pressure caused by wind on the car might as well be
simulated, once considerable wind velocities can be
achieved on during solar race events held in deserts
such as in Australia and Chile.
ACKNOWLEDGMENT
This research was realized inside the Onda Solare
collaborative project, an action with the aim at
developing an innovative solar vehicle. The authors
acknowledge support of the European Union and the
Region Emilia-Romagna (inside the POR-FESR 20142020, Axis 1, Research and Innovation)
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NOMENCLATURE
Eijk
Tensile elastic modulus
Gijk
Shear modulus
A,B,C
FEM
SF
CFRP
N
Wt
Ww
Fw
f
Wheel hub geometries
Finite Element Method
Safety Factor
Carbon Fiber Reinforced Polymer
Vibration mode number
Weight of the car with passengers
Weight applied on each wheel
Force applied on each wheel
Frequency
VOL. 45, No 3, 2017 ▪ 403
Greek symbols (Times New Roman 10 pt, bold, italic)
Hill-Tsai number
α2
σ ijk
Normal stress
τ ijk
Shear stress
υijk
Poisson’s ratio
Subscripts
1,2,3
I,II,III
rupture
Principal directions
Modes of vibration
Rupture stress
АНАЛИЗА ЕВОЛУЦИЈЕ СИСТЕМА ВЕСАЊА
КОД СОЛАРНИХ АУТОМОБИЛЕ
Ф. Де Камарго, К. Фрагаса, А. Павловић,
М. Мартињани
404 ▪ VOL. 45, No 3, 2017
Контраст између модерних алтернатива мобилности
и потражње одрживости био је битан фактор за
индустрију у последњих неколико деценија,
подстакнут технологијама које су постепено
сужавале ту празнину. Међу њима, соларни
аутомобили представљају савремени тренд за
обезбеђивање
ове
потребе.
С’обзиром
на
комплексност ове технологије, постизање ефикасног
дизајна захтева побољшање сваког аспекта возила,
укључујући његову механику. Критичном улогом у
стабилности возила, систем вешања соларних
аутомобила је детаљно испитан у овом раду,
нарочито еволуција структурног дела која је
директно одговорна за подносење сила којима је
подвргнута каросерије возила. Три различита
облика
реализавана
од
пластике
ојачане
угљеничним влакнима су анализирана и упоређена
статичком и модалном анализом коначних
елемената: две предње виљушке спојене у
јединствени зглоб, а точак повезан са новим
клизним системом.
FME Transactions

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