International Journal of Pure and Applied Mathematics

Volume 118 No. 18 2018, 935-943

ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)
url: http://www.ijpam.eu
Special Issue
ijpam.eu

STRUCTURAL AND MODAL ANALYSIS

OF SCOOTER FRAME
D.Mohankumar1, R. Sabarish1, Dr. M. PremJeyaKumar2.
1 Research Scholar, Department of Automobile engineering, BIST, BIHER, Bharath University, Chennai.
2 Supervisor, Department of Automobile engineering, BIST, BIHER, Bharath University, Chennai.
mohankumar.auto@bharathuniv.ac.in, Sabarish5041@gmail.com, prem.auto@bharathuniv.ac.in,

ABSTRACT – wheels allow the bikes to use tubeless tires, which, unlike
This project discusses the stress and deformation traditional pneumatic tires, don't have an inner tube to hold
developed in chassis during the different load cases and the compressed air.
identifying the failure modes by the modal analysis. It starts Brakes The front and rear wheels on a
from the benchmark study of different scooter frame in the
motorcycle each have a brake. The rider activates the front
aspect of material selection, mechanical properties and the
sections used in it (usually circle section is preferred because brake with a hand lever on the right grip, the rear brake
of its easiness of manufacturing ,even load distribution for with the right foot pedal. Drum brakes were common until
different load Cases and some other geometrical reasons) the 1970s, but most motorcycles today rely on the
Then Structural and modal analysis of frame under the superior performance of disc brake.
various load consideration It involves 3d Modeling in Pro-E,
Meshing in Hyper mess and analysis in ANSYS.
Thus the aim of the project is following: II .METHODOLOGY OF THE STUDY:
a) To validate the Frame design i.e. stress and
deformation calculation using FEA and suggest the design Take the benchmark of different scooter
recommendations frame for the Tube thickness, Tube diameter and mounting
b) To do Bench mark study of the frame structure, load position brackets along with thickness. Collect the material
characteristics, metallurgical and mechanical properties of property of the Frame and its allied parts. Carry out the
the scooter frame members. design calculations and assume the required parameters.
c) Identify critical stress areas and suggest for
Model the frame structure in the PRO ENGINEER for
design improvement from the Modal analysis by identifying
the different mode shapes and Natural frequency of the different dimensions. Finite Element Meshing of these
frame. models to be carried out in HYPERMESH. The elements
properties can be defined either in the HYPERMESH or in
the ANSYS.
I. INTRODUCTION In this project I have defined the elements and load
parameters at hyper mesh itself[5-8].
The two-wheeler chassis consists of the frame, These meshed models are taken in to the ANSYS solver
suspension, wheels and brakes. The chassis truly sets the for solving. Record the results and analyse the same
overall style of the two-wheeler. Automotive chassis is the
main carriage systems of a vehicle. The frame serves as a A. Development Of 3d Models - Computer Aided Design
skeleton upon which parts like gearbox and engine are (Cad)
mounted. It can be made of steel, aluminum or an alloy. It Creating an accurate geometric model is the first key step
is essential that the frame should not buckle on uneven in a finite element process. It stands to reason that if the
road surfaces and that any distortions which may occur geometric model does not accurately represent the physical
should not be transmitted to the body. The frame must object, the analysis will be incorrect. Many CAD models
therefore be torsion resistant[1-4]. work fine for the design and drafting but they do not have
The frame consists mostly of hollow tubes and the quality required for FE meshing operations. So a
serves as a skeleton on which components like the gearbox special care must be taken during the modelling of the
and engine are mounted. model in the meshing point of view.
Suspension The frame also serves as a support
for the suspension system, a collection of springs and B. Fundamentals of fea (finite element analysis)
shock absorbers that helps keep the wheels in contact with
the road and cushions the rider from bumps and jolts. The FEA process is a method of analysing a part or
Wheels Motorcycle wheels are generally assembly to ensure performance integrity over the
aluminium or steel rims with spokes, although some product’s lifetime. FEA allows engineers to simulate
models introduced since the 1970s offer cast wheels. Cast structural behaviour, make design changes and see the

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International Journal of Pure and Applied Mathematics Special Issue

effects of the design changes quickly or even automatically.

This process is a computer simulation of the make them III. BASICS OF FE THEORY
and brake them or build them and bust them process in
which a physical prototype is built and tested, and then A.Determination Of Natural Frequencies And Mode
rebuilt and tested as often as necessary until an acceptable Shapes
design is created. This physical process can be costly and
time consuming. But FEA does not replace testing. FEA Assuming a harmonic solution {x} = {}
supports and enhance testing. It especially helps to reduce sin t and determining its first and second derivatives the
the number of still necessary-physical tests. FEA and following forms are obtained from the upper equation
testing should be used together because each -2 has
[M] unique
{} sint + [C] {} sint = 0
strengths[9-15].
([C] -  [M])){} = 0
2

All types of finite element analyses involve

Setting 2 =the
 the eigenvalue problem reduces to
same basis steps as described
[C - i M] {i} = 0
with
{i} = a eigenvector (or mode shape) corresponding to an eigenvalue i
Geometric Modelling
{The natural or characteristics frequency)
For each eigenvalue, which is proportional to a natural
frequency, there is a corresponding eigenvector or mode
Finite Element
Modelling (Meshing) shape. The eigenvalues are related to the natural
frequencies according to
fi = i / 2 = i / 2
Due to the orthogonality of the calculated modes, none of
Define the the modes is affected by any other mode. That means that
Environment each mode is characteristic by itself, it cannot be described
by a linear combination of the rest of modes. Each mode
shape is similar to a static displaced shape as there are
displacements and rotations for each node. However, there
is one important difference between a mode shape and the
Perform analysis static displacements: the scaling. In static analysis the
displacements are the true physical displacements due to
the applied loads. Since there is no applied load in normal
mode analysis, the mode shape components can all be
Assess Results scaled by an arbitrary factor. Normally this scaling is done
so that the maximum displacement in any mode is 1.0
Furthermore the shape function which can be linear or non IV.GEOMETRY, DESIGN AND MANUFACTURING
linear of an element influences its ability to represent CONSTRAINTS:
displacements or stresses that vary over the element edges A. Target Specification:-
or surfaces and thus contributes directly to the quality of
the analysis results[16-23]. The choice of a proper finite
element is crucial for simulating correct structural
behaviour.
Meshing is the process of subdividing the
geometry in to a series of discrete elements. It is done to
represent complex geometry and provide more elements in
regions of interest, which for example are those where,
stress gradients or structure born noise are greatest

Wheel base 1310mm

. Ground clearance 150mm
Seat height with cushion 760mm

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International Journal of Pure and Applied Mathematics Special Issue

Seat base height 660mm Poisson’s Ratio (PRXY) : 0.29

Vehicle power 1200watts Density: 0.00000785 kg/mm3
Battery 24Ah x 4Nos Ultimate tensile strength : 520 N/sqmm
Engine 75cc Yield strength: 360 N/Sqmm
Castor angle 25 degree STD : IS – 3074 ; CEW 1 steel tube for Auto motive
Trial Approx. Main tube outer diameter: 48mm ;Thickness :3mm
10mm Long member : Refer below for elliptical section
Offset 42mm dimensions
Weight of frame 12 kg (1.6mm thick) Section: Elliptical & circular; Thickness: 1.6mm & 2mm
14 kg (2mm thick) Dimensional details of elliptical section:
Wheel centre to shock absorber mounting angle
20degree
Ground clearance Approx, 150mm

B. Strength and stiffness requirement:

It is governed by static & dynamic loads acting

under various conditions like high speed cornering, driving
over irregular roads and driving over bumps and potholes.
Apart from the above, there are other loads like rider and
pillion, fuel tank and other vehicle parts. The frame
stiffness shall be such that the deflection is minimum
during various operating conditions. Typical values of
Section modulus of elliptical section (2mm thick)
frame stiffness are taken from benchmark vehicles and
:1.697e03 & 2.12e03
further fine-tuned based on vehicle handling simulation
Section modulus of elliptical section (1.6mm thick)
using multi-body software like ADAMS. Inadequate frame
:1.41e03 & 1.71e03
stiffness leads to vehicle instability in cornering and
Section modulus of circular section (1.6mm thick) ;od
affects handling and manoeuvrability. The strength of
41mm:1.9e03
frame shall be such that there is minimum permanent
deflection during operating conditions. In order to ensure
A. Meshing In Hyper mesh
that, finite element analysis is done and the stress levels
The following are the no of elements and the nodes crated
are calculated. The strength of the frame [frame tubes] is
for the different models
fixed at a value that is more than the stress value obtained
(For both elliptical and round long member) after the
during analysis[24-29].
meshing
C. General stiffness requirement for motorcycles and
scooters

V. STRUCTURAL AND MODAL

ANALYSIS OF SUSPENSION FRAME
No Of
USING ALLOY STEEL Sno Model Name No Of Elements
Nodes
Scooter frame-
A. Material properties
1 elliptical long 215849 215199
member
Young’s Modulus (EX) : 205000N/mm2

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International Journal of Pure and Applied Mathematics Special Issue

Scooter frame-
2 round long 213387 213011
member

following are the properties of the elements selected for

meshing

Element Type:
SHELL 181
MPC 184
B. SHELL 181 Element Descriptions

SHELL181 is suitable for analysing thin to

moderately-thick shell structures. It is a four-noded
element with six degrees of freedom at each node:
translations in the x, y, and z directions, and rotations
about the x, y, and z axes. The degenerate triangular option
should only be used as filler elements in mesh
generation[30-33].

VI. LOAD AND BOUNDARY CONDITION

B . Von Misses stress plot

The above load condition established by Considering the 2

person with 103kg is sitting at rear and a kit having 25 kg
is travelling in the scooter. 30% of load from rider mass
distributed to handle bar/head tube area as a thumb rule of
the design. battery mass 45kg totally 278 kg and in 2g
condition 556 kg
Degrees of freedom are fixed at front and rear Wheel
centre positions. The same environment created and
analysed in the ansys for the various thickness and sections
of the frame configuration[34-36].
VII ANALYSIS RESULT

A Displacement plot Summary of Vertical and Lateral load results

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International Journal of Pure and Applied Mathematics Special Issue

IX Modal analysis plot

VIII. FRAME ANALYSIS UNDER THE CORNERING

LOAD
This study conducted to analyze the lateral
stiffness of the frame particularly from the front cornering Mode-1
load. As a thump rule 10% of overall load can be taken as
a applied load.

Bench mark frame

Mode-2
Bench mark frame subjected for cornering load as
shown above and verified against the values of FEA. To
validate the correlation %

maximum maximum
disp. disp.
Measured Measured Correlation %
at lab at FEA
(mm) (mm)

Deflection 12 9 75 %
(mm)

Deflection under Corner Load –FEA

Mode-3

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International Journal of Pure and Applied Mathematics Special Issue

All four combination modal analysis results

shows that, there is no much variations in the natural
frequency. And they are not matching with the engine
Mode-4 fundamental firing frequency orders. And Human is
sensitive in the frequency band of 4 -9 Hz. And the result
shows , observed frequencies are not harm to the human
body also placed in the com fort level.

IX.CONCLUSIONS

Thus a scooter frame is designed for elliptical and

round cross section with in the specified Geometrical
boundary condition
The same were tested and verified with Finite
Mode-5 element analysis for vertical and lateral load condition .
Bench mark study for both material selection and behavior
of frame under the various load condition studied. The
generated shear stresses are less than the permissible value
so the design is safe. Design improvements are made in
order to meet the maximum targeted stress value of 300
MPa and vertical displacement less than 18 mm based on
the bench mark study.
The usage of elliptical cross section thus increase
the vertical stiffness also improves the manufacturability
aspects in terms of pipe joints welding.
Lateral stiffness is very much important for the
cornering behavior of the vehicle.
We should also ensure that the lateral stiffness is well in
the acceptable level
Mode-5 For that lateral loading analysis and modal analysis has
done.
The above shown results are for the frame made of In lateral load condition the frame is having
elliptical 2mm thick long member sufficient stiffness also the stress induced in the sections
Similar results are observed in all the other 3 cases like also within the limit by comparing with bench mark data
circular1.6mm thick,eliptical 1.6 &2mm thick longmember. collected
From modal analysis the Identified natural
frequencies for different mode shapes are not equal to the
single cylinder engine's fundamental firing frequency
orders
also not sensitive and in comfort zone with respect to the
sensitive human body frequencies.
Henceforth I propose the elliptical cross section
for hybrid scooter as the hybrid scooter frames are

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International Journal of Pure and Applied Mathematics Special Issue

subjected to both statically mounted battery and engine 8. Udayakumar R., Khanaa V., Saravanan T., Saritha G.,
loads. Cross layer optimization for wireless network (WIMAX),
As part of cost elliptical sections are costly also not widely Middle - East Journal of Scientific Research, V-16, I-12,
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X. SCOPE FOR FURTHER WORK
system, Middle - East Journal of Scientific Research, V-
 The natural frequency of vibration obtained can be further 16, I-12, PP-1798-1800, 2013
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a Khanaa V., Mohanta K., Saravanan T., Comparative study
whole considering all the components of the motorcycle. of uwb communications over fiber using direct and
external modulations, Indian Journal of Science and
 As a scope for the further work on this project a complete Technology, V-6, I-SUPPL.6, PP-4845-4847, 2013
harmonic analysis of the assembly can be carried out to 11. Kumarave A., Udayakumar R., Web portal visits patterns
determine the vibration characteristics of the motorcycle predicted by intuitionistic fuzzy approach, Indian Journal
assembly under the influence of engine disturbance, of Science and Technology, V-6, I-SUPPL5, PP-4549-
human weight and road condition. 4553, 2013
12. Thooyamani K.P., Khanaa V., Udayakumar R., An
 The vibration experienced by the rider through the
integrated agent system for e-mail coordination using jade,
handlebar and the footrest can be studied and suitable
modifications can be made in the components of the Indian Journal of Science and Technology, V-6, I-
motorcycle to bring the range of the vibration under the SUPPL.6, PP-4758-4761, 2013
comfort zone. 13. Sengottuvel P., Satishkumar S., Dinakaran D.,
Optimization of multiple characteristics of EDM
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International Journal of Pure and Applied Mathematics Special Issue

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