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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

Dynamic Study of Bicycle Frame Structure

M.S.M. Sani1,2*, N.A.Nazri1, S.N.Zahari1, N.A.Z. Abdullah1, G.Priyandoko1

1
Advanced Structural Integrity and Vibration Research (ASIVR), Faculty of
Mechanical Engineering, Universiti Malaysia Pahang,
26600 Pekan, Pahang, Malaysia
2
Automotive Engineering Centre (AEC), Universiti Malaysia Pahang,
26600 Pekan, Pahang, Malaysia.

E-mail: mshahrir@ump.edu.my

Abstract. Bicycle frames have to bear variety of loads and it is needed to ensure the frame can
withstand dynamic loads to move. This paper focusing on dynamic study for bicycle frame
structure with a purpose to avoid the problem regarding loads on the structure and to ensure the
structure is safe when multiple loads are applied on it. The main objectives of dynamic study
are to find the modal properties using two method; finite element analysis (FEA) and
experimental modal analysis (EMA). The correlation between two studies will be obtained
using percentage error. Firstly, 3D model of mountain bike frame structure has been draw
using computer-aided design (CAD) software and normal mode analysis using MSC Nastran
Patran was executed for numerical method meanwhile modal testing using impact hammer was
performed for experimental counterpart. From the correlation result, it show that percentage
error between FEA and EMA were below 10% due to noise, imperfect experiment setup during
perform EMA and imperfect modeling of mountain bike frame structure in CAD software.
Small percentage error differences makes both of the method can be applied to obtain the
dynamic characteristic of structure. It is essential to determine whether the structure is safe or
not. In conclusion, model updating method is required to reduce more percentage error
between two results.

1.0 Introduction
A bicycle is a light structure that has to support a much heavier weight which is the cyclist [1]. There
are few consideration need to be taken in the process of making bicycle frame which are support loads
of cyclist, surrounding wind and friction. A major concern in analysing practical mechanical structures
is to reliably identify their dynamic characteristics, i.e., their natural frequencies and vibration mode
shapes. These vibration characteristics are needed in order to achieve effective design and control of
the vibrations of structural components [2]. While designing any mechanical system or structure, it is
important to do structural design and analysis, since it can predict the mode shapes and the natural
frequencies to the expected excitation. It is necessary to know the natural frequency of the structure to
model the construction that will not be excited between these frequencies band, if the structure is
excited at one of this frequencies, the resonance will occur [3]. Looking into technical view, the
weight, stiffness and comfort of a bike are three crucial criteria that still drive most new developments.

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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

Steel, titanium and aluminium are materials that commonly used in the industry but carbon fibre
turned to be the most popular material chosen for frames and for almost all bike components [1].
Dynamic study seems necessary to ensure the ability of bicycle frame to endure multiple loads. The
components and the frame are subjected to time-varying force excitations dictated by the cyclist and
by the road. Frame of bicycle is the substantial component of any type of bicycle, to which the saddle,
handlebar and wheels are all attached together. Over the course of improvement of the bicycle, frame
has been widely invented with various designs and made from miscellaneous types of materials. Good
construction of geometric design result in a durable frame while deducting the cost of materials
required, lessened the weight and deducted the usage of material [4]. The light weight of bicycle frame
will contribute in minimizing the energy consumption up hills or during acceleration. There are three
measurements for bicycle frame geometry, which is head tube angle, fork trail and fork rake which
become as the backbone and involved in order to assure the strength of the dynamic structure of
bicycle frame.
For this paper, theoretical approach applied the method of Finite Element Analysis (FEA) by
acquiring data of natural frequencies and mode shape with a purpose to rectify the dynamic structure
of bicycle. FEA involved the usage of CAD Simulation to draw the frame following mountain bike
measurement with aluminium material as shown in Figure 1. It is software that enables the adoption of
finite element analysis FEA besides authorize user to analyse the structural properties like stress,
displacement, and natural frequency [5]. In this paper, modal properties are identified using both
methods which are finite element analysis (FEA) and experimental modal analysis (EMA). FE model
will undergo normal mode analysis in order to choose the most reliable model. From the result
obtained, model updating will be carried out to improve correlation between experiment and numerical
counterparts.

Figure 1. CAD of bicycle frame

2.0 Finite Element Analysis (FEA)

FEA is one of the numerical solutions and significant in introductory treatments. In case of structural
failure like a wrinkling, FEA may be used to help fix the design modifications to meet the new
condition and optimize the parameters [6]. In MSC Patran was used to design finite element model of
the structure and MSC Nastran which is post processing solver utilized for vibration analysis. In this
project, FEA is study in terms of normal modes analysis for bicycle frame structure, with material
properties as tabulated in Table 1 and the result is displayed in Figure 2 below.

Table 1. Properties material of Aluminium

DATA VALUE
Material Aluminium
Density 2700 kg/m3
Poisson’s ratio 0.34
Modulus Elasticity 68.3 GPa

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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

Figure 2. Modeling of structure in FEA

Two modal properties are obtained which are natural frequency and mode shape. The normal
mode analysis module allows computing normal modes of an input atomic or EM structure as well as
an interactive visualization of the computed modes by animating displacement of the structure along
the modes. Besides, the evaluation of the natural frequencies and the corresponding mode shapes plays
a crucial role in vibration analysis since it provides a great deal of information concerning the dynamic
characteristics of a system. Natural frequency results that have been gain from the FEA that has been
run using MSC Nastran/Patran as is displayed in Table 2 below. Meanwhile Table 3 presents the result
for mode shape in which mode 1 and 2 experienced bending, mode 3 faced torsional 1, mode 4
undergone torsional 2 and for mode 5, the condition is torsional and bending.

Table 2. Result of natural frequency for FEA

MODE NATURAL FREQUENCY (Hz)

1 82.71
2 106.2
3 258.46
4 291.01
5 312.48

Table 3. Result of mode shape for FEA

MODE MODE SHAPE MODE MODE SHAPE

1 4

2 5

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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

3.0 Experimental Modal Analysis (EMA)

Modal testing is carried on in order to do vibration testing regarding natural frequency, mode shape
and damping ratio which can be described as EMA. This testing consists of two phases which is
experimental and numerical with purpose to complete the modal analysis process [7]. Impact hammer
testing is applied as the system was provided with energy, parameters were evaluated by fitting the
curve in the transfer function and there is multiple ways to predict the modal parameter indeed. This
test has a function to covert time history signals collected from impact hammer and accelerometers
sensor into frequency spectra the Fourier transformation was used. The ration of Fourier transformed
output and input signals were obtained using Frequency Response Functions (FRF) [8]. Figure 3
below shows the example of impact hammer test for EMA.

Figure 3. Impact test for EMA

ME’scopeVES software is needed for modal testing in which this software can be utilized to
examine and figure out noise & vibration complications in machinery and structures using either
experimental or analytical data. The values for natural frequency and mode shape were obtained as
shown in Table 4 and Table 5 respectively using curve fitting method where the values were taken
based on the nearest value to the FEA obtained previously. Result acquired from EMA was performed
using roving accelerometer method whereas the accelerometer will change according to the node point
that has been set on frame structure.

Table 4. Result of natural frequency from EMA

MODE NATURAL FREQUENCY (Hz)

1 76.4
2 107
3 287
4 300
5 323

Table 5. Result of mode shape from EMA

MODE MODE SHAPE MODE MODE SHAPE

1 4

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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

2 5

4.0 Comparison between FEA and EMA

As both method undergone different methods for obtaining result, there were errors existed. The result
of percentage error displayed for all 5 modes between FEA and EMA was tabulated in the Table 6 and
comparison of mode shape for both analysis is displayed in Table 7 below.

Table 6. Percentage errors of natural frequencies between EMA and FEA for each mode

NATURAL FREQUENCY (Hz)

MODE ERROR (%)
EMA FEA
1 76.4 82.71 8.26
2 107 106.2 0.75
3 287 258.46 9.94
4 300 291.01 3.00
5 323 312.48 3.26

Table 7. Comparison of Mode Shapes between FEA and EMA

MODE SHAPES
MODE
FEA EMA

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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

Correlation is a process to evaluate how close the FE model resembles the reality or in other
words, how good the FE model agrees with the experimental model [9, 10]. It is a good agreement
when the discrepancies is small [11]. From this experiment, percentage of error showing a good result
between EMA and FEA as the error in this experiment is below than 10%, and the discrepancies is
small due to few factors such as noise, imperfect experiment setup during perform EMA and imperfect
modelling of mountain bike frame structure in CAD software. Noise due to knocking process during
EMA is possible to delay until the structure is fully stop and no more vibration left before proceed to
the next knocking process since small vibration on the frame structure is invisible. This also took
longer time to complete the process of knocking in order to finish all the 33 node points on the
mountain bike frame structure. Hence, the number of node point should be increase in order to get
more accurate mode shapes. However, for better correlation between these two analysis, modal
updating is needed to take in action.

Imperfect experiment setup while performing EMA also affected the results of natural
frequency and mode shapes. Among the imperfectness is when the accelerometer is not correctly
placed on frame, the position of frame mountain bike not stable when hanging and other part of
mountain bike that cannot be removed. Besides, it is quite complicated to get an exact modelling of
mountain bike frame structure in CAD software due to a little problem while carry on measurement of
actual mountain bike frame since unavailability of special tool to do measuring.

5.0 Model Updating

The ambiguity in the results among the Finite Element Analysis (FEA) and the Experimental Modal
Analysis (EMA) is due to the expectations made in defining inappropriate element material property
and geometrical property [12]. Model updating is focused with the adjustment of finite element
models by altering data of dynamic response from test structures and updating a finite element model

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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

of a structure so that it can assume more accurate dynamics of a structure [13,14]. The main objective
of model updating is to decreases the imprecision in the finite element model and blunders in expected
results acquired from inaccurate modelling of the boundary conditions and damping, for example [15].
In model updating, the selection of updating parameter is the most important task. There are two
methods of model updating which are direct method and sensitivity method [16]. Model updating will
be acted as an optimization method and is being presented using the structural optimization capability
[17].

In order to decrease the problems in FEA, model updating is conducted to the data of finite
element by applying the first-order optimization method. The optimization algorithm in MSC,
NASTRAN (SOL200) is utilized in this study. The main goal function for the prediction error can be
formulated as
𝟐
𝒘𝒆
𝒈 (𝒙) = ∑𝒏𝒊=𝟏 𝑾 (𝒘𝒂𝒊 − 𝟏) (1)
𝒊

where 𝒘𝒆𝒊 and 𝒘𝒂𝒊 are the experimental and computational natural frequencies respectively, with W as
the real positive weighing factor. The prediction of the modal data is bestowed for detraction in the
updating operation. The operation prolongs until convergence is achieved, where the contrariness
between values of g(x) from the following iteration is adequately small [10]. Three crucial parameters
are chosen for updating which are Young Modulus (E), Poisson Ratio (ѵ), and density (ρ). The
original value for Young Modulus, Poisson Ratio and density are 68.3 GPa, 0.34 and 2.7 kg/m3
respectively. For updating, upper and lower bound values for Young Modulus are 64.9 GPa to 71.7
GPa. Otherwise, for Poisson Ratio, the values are 0.306 to 0.374. Meanwhile for density, 2.43 kg/m3
to 2.97 kg/m3. Result of model updating can be seen as in Table 8 below.

Table 8: Comparison of natural frequency between initial result and updated result

Initial FEA Result Model updating FE Result

Mode EMA
Frequency (Hz) Frequency Error (%) Frequency Error (%)
(Hz) (Hz)
1 76.4 82.71 8.26 83.85 9,75
2 107 106.20 0.75 107.67 0.63
3 287 258.46 9.94 262.86 8.41
4 300 291.01 3.00 294.99 1.67
5 323 312.48 3.26 316.6 1.98
Total Error 25.20 22.44

As shown in Table 8 above, it is clear that the initial value of FE result and model updating
result for natural frequency show dissimilarities. Percentage of errors shows diminishing result. As the
summary, updating result succeed by deducting the value of errors compared to the initial result.

6.0 Conclusion
As the conclusion, problems of every close modes frequently arise in engineering practice due to
structure symmetries with little damping and the accurate determination of the modal parameters. It is
suggested to make sure removed all the part at bicycle frame using appropriate tool and use a correct
tool to measure actual dimension of bicycle frame. This is because; dimension plays an important role
to modelling an accurate bicycle frame. The percentage differences between finite element analysis
(FEA) and experimental modal analysis (EMA) are below 10%. Natural frequency acquired from

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International Engineering Research and Innovation Symposium (IRIS) IOP Publishing
IOP Conf. Series: Materials Science and Engineering 160 (2016) 012009 doi:10.1088/1757-899X/160/1/012009

EMA and FEA shows small percentage error differences makes both of the method can be applied to
obtain the dynamic characteristic of structure. After updating results, the total errors between FEA and
EMA are lessened and objective of model updating is achieved.

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