Optimal Design of Electric Motorcycle Tubular Frame using Topology
Optimization
KAMIL STENCEL, MARIOLA JURECZKO
Department of Theoretical and Applied Mechanics, Faculty of Mechanical Engineering,
Silesian University of Technology,
Konarskiego 18A, 44-100 Gliwice,
POLAND
Abstract: - This paper proposes a methodology for designing motorcycle tubular frames using simulation
software such as MATLAB/Simulink and ANSYS, which provides an efficient and cost-effective way to
approximate loads acting on the structure and topology optimization to meet performance and safety
requirements. Using these tools, the design process can be simplified and reduce the number of costly physical
prototypes and tests. The multi-body model developed in MATLAB® Simscape was used to approximate the
loads and boundary conditions on the frame, while the ANSYS software was used for topology optimization.
The resulting motorcycle frame was found to weigh 9.48 kg. The simulation results also showed that the
proposed frame design met the required safety and performance criteria. The methodology presented in this
paper is not limited to electric motorcycle tubular frames and can be applied to other types of vehicle frames or
structures. The use of simulations allows for the exploration of different design options and the identification of
optimal solutions with minimal cost and effort. The combination of MATLAB® Simulink and ANSYS is a
powerful tool for the design and optimization of complex structures, providing accurate results and saving
valuable time and resources.
Key-Words: - Electric Vehicle, Motorcycle, Single-Track Vehicle, Frame, Finite Element Analysis, Topology
Optimization, Design Space, Non - Design Space, Limiting Conditions
Received: February 19, 2023. Revised: July 17, 2023. Accepted: August 23, 2023. Published: September 14, 2023.
1 Introduction
The growing emission of air pollutants is
increasingly affecting global trends. Products and
services that do not negatively affect ecosystems or
limit this impact are perceived positively by
recipients. Due to good public opinion, you can see
a positive effect on the sale of such goods, while
legislators in many countries offer legal and tax
relief for entities using them. As a result, many
industries are looking for new technologies through
which environmental degradation can be minimized.
The transport sector is no exception in this case, as
shown by the research and forecasts of the
International Energy Agency. According to the
Electric Vehicle Initiative (EVI), a multi-
governmental policy forum created in 2010 under
the Ministry of Clean Energy Program (CEM), more
than 26 million electric cars were on the road in
2022, up to 60% relative to 2021 about three times
more than in 2020 and more than four times in
2019, [1], [2].
Electromobility trends also apply to two-
wheelers, which, thanks to zero-emission drives
with energy recovery systems, are perfect for both
urban and rural areas. Therefore, the average range
of electric motorcycles, which is around 100 km,
guarantees, with a safe margin, an ecological
alternative in the private transport sector. Low noise
emissions and zero pollutant emissions increase the
comfort of living in urban and rural areas. The
growing demand for the product results in the
development of the industry and the innovation of
the solutions offered. The successes of racing series
such as the ABB FIA Formula E or MotoE World
Cup, which are a testing ground for solutions in the
field of electric drives, show the interest in the
technology of both the public and manufacturers
developing the products offered. The new niche
created in this way allowed newly established
manufacturers, such as Tesla Inc. to quickly
stabilize their position on the market. or Zero
Motorcycles, which confirms the possibility of
entering the market with a proprietary product.
According to, [3], [4], the construction of the
motorcycle frame plays a key role in ensuring the
optimal performance and safety of the vehicle. The
frame of all single-track vehicles is a kind of
skeleton to which other components are mounted.
Its main tasks are to ensure the required rigidity and
strength of the entire vehicle structure, as well as
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shock and impact resistance to the vehicle. Due to
this, it protects the driver and the most important
elements of the vehicle. In, [5], the authors
discussed studies that aim to centralize the load and
reduce the load on the frame. This has been
achieved by optimizing the weight distribution of
the frame so that its center of gravity is below the
rider's path. Also, in the article by, [6], a two-step
process of designing a motorcycle frame is
described. The authors showed how important the
design process was to join with a numerical analysis
of stereo mechanicals to obtain the optimal mass of
the construction; a simultaneous fulfillment of the
strength conditions was observed. In, [7], the
authors focus on the chassis of an electric
motorcycle. They analyzed both the different types
of frames used for the motorcycle chassis and the
different materials. Then they performed static
analysis, modal analysis, side impact, and front
impact analysis in CAE software for different
loading conditions. They also showed that the use of
topological optimization to minimize mass increases
the efficiency of the entire construction process.
Optimization involves organizing activities and
processes in a way that maximizes the effects while
minimizing costs. Optimization has long been
successfully applied in industry, increasing the
efficiency of technological processes, and
improving the quality of products. Using computer
methods, optimization finds ever-widening
applications in the design phase, allowing designers
to improve the mechanical parameters of structures,
reduce weight, and decrease project volume,
resulting in more efficient use of resources. Before
the use of computers, the optimization possibilities
were limited, and finding the best solution often
involved minimizing weight by reducing cross-
sectional dimensions, using materials with better
parameters, and limiting shape optimization.
With the progress of computing techniques,
topology optimization has become a powerful tool
for designing optimal structures that meet the
criteria adopted by the decision-maker. In, [8], the
authors presented the process of formulating an
optimization task as a topology optimization model
considering material strength, structural stiffness,
and structure stability. On the other hand, the
research by The study, [9], concerns the application
of topology optimization to minimize the mass of
various structures. Topology optimization in
engineering applications most often consists of
reducing the weight of the structure, considering the
strength of the material, the stiffness of the
structural structure, and the stability of the entire
structure. This type of optimization combined with
the design process significantly reduces costs and
eliminates design failures. In the case of vehicle
design, the use of topological optimization results in
a weight reduction and increased stiffness of the
structure, with positive effects on many other
aspects, such as reduced energy consumption,
improved traction, and mechanical durability, as
well as improved dynamic properties. Therefore, it
is desirable to subject designs to optimization
processes that lead to products with better
parameters. In, [10], the authors describe their
research that involves a comparative analysis of
three types of frames: a conventional lattice frame, a
generative frame, and a topology optimization one.
In, [11], the authors presented the formulation of the
quad bike frame topology optimization problem,
also discussing the specific properties of the design
space and the specific cases of its loads. Typical
design and manufacturing framework that involves
the combination of topology optimization and 3D
printing are presented in, [12]. The authors
discussed this process in the example of a scooter
frame.
This study aims to expedite the design process
of an electric motorcycle frame by harnessing the
potential of topology optimization. Traditional
design methods for vehicle frames can be time-
consuming and labor-intensive, often requiring
numerous iterations and physical prototypes to
achieve an optimal design. In contrast, topology
optimization offers a more efficient approach by
automating the search for the most effective
material distribution within the frame. By utilizing
topology optimization in the design of the electric
motorcycle frame, the study seeks to reduce the
number of trial-and-error design cycles and
accelerate the identification of an optimal structure.
The software-driven optimization process analyzes
the load distribution, boundary conditions, and
performance objectives, aiming to find the most
efficient material arrangement that meets safety,
performance, and weight requirements. The study
endeavors to demonstrate the effectiveness of
topology optimization in streamlining the design
process while maintaining or even enhancing the
structural integrity and mechanical performance of
the frame. By identifying the ideal material layout, it
becomes possible to create lightweight and
mechanically robust frames, leading to improved
energy efficiency and overall performance of the
electric motorcycle. Through a combination of
numerical simulations and experimental testing, the
performance of the optimized frame was evaluated
and compared to conventional motorcycle frame
designs. The results of this research can
significantly accelerate the process of designing
motorcycle frames and provide information on the
possibilities of using topology optimization in other
engineering applications.
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2 Formulation of the Topology
Optimization Problem
In, [13], the authors discussed the theory concerning
both the idea of topology optimization and various
methods for the optimal design of topology, shape,
and material for mechanical structures. This book
also describes many practical applications of
topology optimization to optimize the size and
shape of mechanical components.
Topology optimization is a process whose task is to
optimize the shape of a mechanical structure in a
predefined 2D or 3D, [14], [15], [16], geometrical
design space (domain Ω in or ), with
boundary conditions imposed by the designer. The
optimized structure is subjected to external loads
and must satisfy many conditions defined by the
designer, such as strength, stiffness, and stability.
The main idea of this optimization method is the
percentage distribution of the initial mass of the
optimized structure in a predefined design
space/domain such that a global measure takes a
minimum. Topology optimization is a numerical
method that involves modifying the shape
(topology) of a designed part in such a way that
areas that do not transfer loads are removed.
Two groups can be distinguished in topology
optimization:
General shape optimization is applied in the case
of details with a specified working area, in
which, during the optimization process, areas
filled with material that transfer loads are
separated from areas that do not transfer loads
and are therefore being emptied.
System optimization is used in the case of beam
structures, where the solution consists of the
truss system and cross-sections of individual
beams.
Conventional topology optimization uses finite
element analysis to evaluate design performance and
create a mechanical structure that meets the imposed
conditions. The predefined geometrical design space
is also discretized using the finite element method,
which allows to representation of the distribution of
the structure material and simulates its deformations
under the influence of applied loads. A discussion of
the different methodologies used by many
researchers in topological optimization can be found
in, [17].
The subject of the optimization presented in the
article is the motorcycle tabular frame, which we
treat as a solid body. The deformation of such a
body model under certain load conditions can be
represented using the linear elasticity mathematical
notation. To apply the linear theory of elasticity,
[18], [19], small deformations (or strains) and linear
relationships between the stress and strain
components are assumed. The equations for the
linear elastic boundary value problem are based on
the equilibrium equations, stress-strain relations,
and stress-displacement relations.
The equilibrium equations have the form:

in
V
(1)
where:
 the independent stress tensor,
body force,
V
the volume of the elastic body.
For linear elasticity, the stress-strain relationship
takes the form:
  in V (2)
or
  in V (3)
where:
 the independent strain tensor,
 elastic constant,
 compliance constant.
The strain energy density and complementary B
we can define as:

, (4)

, (5)
which satisfies the following energy identity:
. (6)
For linear elasticity, the stress-displacement
relationship takes the form:

  in (7)
where:
the displacement component,
indicates that the surface integrals are to be
taken over that part of the surface only where
the appropriate displacement is prescribed.
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The boundary conditions for the considered
optimization task can be presented as follows:
For given surface displacement:
in (8)
where:
displacement component on the boundary
For given external load on boundary surface:
 in (9)
where:
indicates that the surface integrals are to
be taken over that part of the surface only
where the appropriate surface stress is
prescribed
external force on the boundary
the total boundary surface equals:
. (10)
The authors used the Hu-Washizu variational
principle, in which, according to, [19], [20], [21],
three types of variables are independent of each
other, and the strain-stress relationships are
variational constraints:

󰇧 
 󰇨


󰇛󰇜
(11)
To carry out the vulnerability (eq.11) minimization
process, it is necessary to set constraints:
The size of the available mass m0 must satisfy
the equation:
 (12)
where:
- volume density V assuming homogeneity.
3 Problem Solution
To be able to perform the topological optimization
of the motorcycle frame, it was necessary to start
with the development of its CAD model. Figure 1
shows the assumed geometry of the supporting
structure.
Fig. 1: CAD model of the motorcycle with the
assumed geometry of the supporting structure
The design domain, also known as the analysis
domain, is the spatial region where structural design
optimization is performed. It defines the geometric
space where material distribution can be modified to
achieve an optimal design. The shape and size of the
design area are important factors that have a
significant impact on the optimization process. A
well-defined design area is essential to ensure that
the optimized structure resulting from it meets the
performance requirements and requirements
required. In topological optimization, the material
distribution in the design domain is represented
using continuous fields that indicate the presence of
the material at each point. This is achieved by
material interpolation techniques, using numerical
functions (usually called design variables or density
fields as discussed in eq.12) to assign values
between 0 and 1 at each point in the domain. A
density value of 1 corresponds to a solid, 0 to an
empty space. The intermediate values indicate the
presence of partial materials, allowing a gradual
transition between solid and void regions. With the
use of the FEA tools the continuous material is
discretized, assigning the values at the nodes of the
model. The design variable field acts as a key
control variable in the optimization process,
allowing the algorithm to shape and evolve the
structural design to obtain the best solution.
3.1 Static Analysis
To optimize the topology, it is necessary to
determine the state of stress in the analyzed
motorcycle frame construction.
Static analysis requires the definition of material
properties, discretization of the geometric model of
the tested structure, which is shown in Figure 2 and
the determination of boundary conditions and loads
(Figure 3).
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The motorcycle frame has six degrees of
freedom, and the balance in a standing position
while riding is maintained by the gyroscopic effect
resulting from the principle of conservation of the
angular momentum of rotating masses, which are
the wheels of the motorcycle. However, considering
the case of a simple load-bearing structure of a two-
wheeler without suspension, it can be concluded that
the wheel axles are the places of frame restraints,
which was proved by the authors in, [22]. According
to the studies, it was decided to fix the frame in the
place where the front suspension and the rear
swingarm were attached.
All these data are also used in the topology
optimization process. The ANSYS software was
used for static analysis using the finite element
method.
Three types of steel were used as materials for
the motorcycle frame: SSAB Docol R8, S355J2, and
S460N. All steels are defined as isotropic and linear
materials, meaning that their simplified stress-strain
curve is a straight line. This approach is not
recommended for calculations where the tested
structure is subjected to heavy loads causing large
deformations. However, when the expected strains
are within the range of Hooke's law, this
simplification has a negligible effect on the results
and significantly reduces the calculation time.
Material properties are listed in Table 1.
Table 1. Material properties
SSAB
Docol R8
S355J2
Density [kg/m3]
7900
7850
Young’s modulus
[GPa]
215
210
Poisson's ratio
0.3
0.29
Yield strength
[MPa]
690
355
Tensile strength
[MPa]
800
490
To determine the value of loads acting on the
supporting structure of the motorcycle, its multi-
body model was developed in MATLAB®
Simscape. Table 2 and Figure 3 show the
determined load values.
Table 2. The load-supporting structure
of the motorcycle
The maximum force acting on the
front suspension in one axis, in N
14453
The maximum force acting on the rear
suspension in one axis, in N
25324
The maximum force acting on pull rod
suspension in one axis, in N
39614
The maximum force acting on the rear
swing arm in one axis, in N
40457
Fig. 2: Discreet model of the motorcycle frame
Fig. 3: Presentation of the loads acting on the model
The motorcycle frame has six degrees of
freedom, and the balance in a standing position
while driving is maintained by the gyroscopic effect
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resulting from the principle of conservation of the
angular momentum of rotating masses, which are
the motorcycle wheels. However, considering the
case of a simple load-bearing structure of a two-
wheeler without suspension, it can be assumed that
the wheel axles are the places of frame restraints.
Scientific publications, [23], [24], [25], describing a
given problem confirm the validity of this
assumption. The only difference in the
considerations of individual scientists is the number
of received degrees of freedom in the places where
the model is fixed. Based on the literature review, it
was decided to fasten in place of frontal suspension
and the independent suspension arm.
During the static analysis, two variants of the
restraint were considered:
The variant I- takes away all degrees of
freedom.
The Variant II - the rear control arm mounting
has one degree of freedom allowing for its
rotation around its axis. In both variants, the
front suspension fixing point has two degrees
of freedom allowing for rotation around and
along its axis.
After defining the boundary conditions and
determining the loads acting on the motorcycle
frame structure, static analysis was carried out in the
ANSYS Mechanical program. Figure 4 and Figure 5
are the stress diagram, the total deformation diagram
under the load condition, and the I variant of the
boundary conditions. The same diagrams for the II
variant of the boundary conditions are shown in
Figure 6 and Figure 7.
Fig. 4: Equivalent Huber-Mises stress diagram the
I variant of the boundary condition.
Fig. 5: Total deformation diagram the I variant of
the boundary condition.
Fig. 6: Equivalent Huber-Mises stress diagram the
II variant of the boundary condition.
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Fig. 7: Total deformation diagram the II variant of
the boundary condition
Comparing the results obtained for both variants
of boundary conditions, it can be seen that the
maximum value of equivalent stress decreased by
7% for the II variant, while the maximum value of
total deformation for this variant increased by as
much as 45% compared to the I variant.
3.2 Topology Optimization
In the context of ANSYS software, topology
optimization is a powerful engineering tool that
leverages the capabilities of the software to optimize
the material distribution within a given design
domain. ANSYS provides a comprehensive suite of
tools and algorithms to perform topology
optimization efficiently and accurately. The process
begins by importing the geometry of the structure
into ANSYS and defining the design domain and
relevant boundary conditions. Users can specify
loading conditions, constraints, and design
objectives, such as maximizing stiffness,
minimizing weight, or optimizing for other
performance criteria. ANSYS employs advanced
optimization algorithms, like the SIMP (Solid
Isotropic Material with Penalization) method, to
iteratively redistribute material within the design
domain. This iterative process gradually removes
less essential material while preserving critical load-
bearing elements. The material density of the design
domain is updated in each iteration, and stress
analyses are performed to assess structural
performance.
Before commencing topology optimization, it is
essential to define its parameters, which include
design space and non-design space, objective
function, and limiting conditions. In this study, non-
design space was defined by surfaces where
boundary conditions and loads were set,
representing the parts of the frame that need to meet
the specific dimensions and shape to accommodate
suspension and bearings. The limiting condition was
defined as the final mass limit of 15% of the initial
value, which was 110.15 kg. The objective function
was to achieve the consistency of the results of the
static analysis after optimization with the results
before optimization. By default, the software defines
the objective function to minimize compliance and,
therefore maximize the rigidity of the structure.
Since the manufacturing methods were not a
limiting factor in this particular case there were no
additional conditions considered. Those can play a
major role in the final shape of many parts that are
made by milling for example.
The resulting geometry of the tubular frame is
shown in Figure 8. Plots of the objective function
and constraint values during each iteration of the
optimization process are shown in Figure 9. The
method utilized a convergence criterion-based
objective function (purple line in the upper plot)
which assumed a certain ratio for the initial and
final model energy during analysis. For the present
case, the program determined the final objective
function value to be at the maximum level of
0.15843, with a value of 0.0316 obtained after the
last iteration (blue line in the upper plot). The
constraint was a maximum of 15% of the initial
mass (blue line in the lower plot).
Topology optimization has been carried out by
using ANSYS.
Fig. 8: Results geometry of the tubular frame
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Fig. 9: The plots of the objective function and the
constraint limit for the iterations of the optimization
process
Fig. 10: Tubular frame geometry based on topology
optimization result
The obtained geometry was then imported into
CAD software, where its shape was replicated while
ensuring the manufacturability of the structure. The
resulting tubular frame geometry is shown in Figure
10, while the comparison of both geometries is
shown in Figure 11.
The optimized construction of the motorcycle
tubular frame weighs 9.48 kg. To verify its strength,
a static analysis was carried out. The boundary
conditions and loads were the same as those in
Table 2, as shown in Figure 12.
The results of the numerical simulations carried out
are shown in Figure 13 and Figure 14.
Fig. 11: Comparison of the structure design with the
result of topology optimization
Fig. 12: The boundary conditions and loads acting
on the model
Fig. 13: Equivalent Huber-Mises stress diagram
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Fig. 14: Total deformation diagram
Based on the obtained results, it can be
concluded that the optimization goal has been
achieved. Compatibility of the results of the static
analysis of the frame structure after optimization
with the results before optimization was achieved.
Limiting conditions were also met - the weight of
the optimized structure of the load-bearing frame
does not exceed 15% of the initial weight. It is
9.48kg which is 8.6% of the initial weight.
4 Conclusion
The proposed methodology presented in this paper
allows for cost and time savings, provided that
sufficient computational power is available. The use
of MATLAB Simulink software for early
approximation of loads acting on structures enables
the quick acquisition of realistic results. The results
obtained in this way make it possible to reduce
costly tests and prototypes and enable an early
application of topology optimization in the design
phase. After defining the workspace, the majority of
project iterations are performed by computer
software, which, with access to adequate
computational power, allows for obtaining geometry
that closely approximates the final design in a short
time. Furthermore, with an appropriate formulation
of optimization parameters, it enables the
preservation of safety coefficients, structural
stiffness, and required mass right from the
beginning. This ensures that the proposed design is
optimally feasible within the given constraints.
In the examined case, a successful optimization
process resulted in a load-bearing structure design
with a mass of less than ten kilograms. For
comparison purposes, the first frame design created
by the authors using comparable materials for a two-
wheeler with similar dimensions weighed 12.5 kg in
its final version. This demonstrates the possibilities
arising from design using optimization algorithms,
which are increasingly applied in the industry.
The presented methodology of the procedures
illustrates a scheme for conducting design work.
The examined case of optimization of the
motorcycle tubular frame can be expanded with
additional simulations imitating component usage,
which would provide further information for
optimization. The topology optimization process
itself should consist of as many iterations as
possible. Based on the experience gained during the
research, the authors also conclude that it is
essential to reproduce the obtained geometry
faithfully. Otherwise, there is a risk of increased
stresses occurring in the structure.
The clear limitation of the usage of topology
optimization during the design process is the need to
design the part manually even after optimization.
Despite the possibility of inclusion of manufacturing
constraints, the commercial software is still not
capable of creating a simple and easy-to-
manufacture shape of a structure. In some cases,
topology optimization may produce designs with
intricate material distributions that are difficult to
interpret or manufacture. While these designs can be
highly efficient in terms of performance metrics,
they may not be practical for real-world
implementation.
The improvement seen by authors in the
researched example, as well as future direction
would be adding parametric optimization on top of
the results of the topology optimization. With a
definition of commercially available circular steel
tubes, the whole structure would be optimized to an
even greater extent. The algorithms responsible for
the topology optimization in ANSYS software are
also a subject of constant development, so the latest
software should be monitored for new possibilities
during the whole process.
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[2] Global EV Outlook 2023 Catching up with
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https://www.iea.org/reports/global-ev-
outlook-2023
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Volume 18, 2023
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WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2023.18.14
Kamil Stencel, Mariola Jureczko
E-ISSN: 2224-3429
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