Study on Dynamic Behaviour of Grass Trimmer
Using Finite Element Analysis
1,2,a *
ZAMAN I., 1ABDURASAD M.R., 1MANSHOOR B.,
1
KHALID A., 3SANI M.S.M
1
Faculty of Mechanical and Manufacturing Engineering, 2Structural Integrity and Monitoring
Research Group, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor, Malaysia
3
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia
a
[email protected]
Keywords: Grass trimmer, finite element analysis, free vibration, natural frequency
Abstract. Nowadays, research on dynamic behavior of structural components is becoming one of
the important parts in the design process for any mechanical system. In order to determine the
dynamic behavior of a vibrating structure, measurements of the dynamic properties of structure are
essential. Free vibration analysis is one of the approaches that apply the finite element method in
determining the structure modes of vibration. Each mode is defined by its natural frequency and
mode shape. In this paper, the free vibration analysis of grass trimmer was performed using
commercial finite element software, such as Ansys®. The importance of determining these
vibration characteristics are crucial as grass trimmer is a common machine that exposed to the
dynamic and static forces coming from the engine and rotating blade. A long term exposure of grass
trimmer's operator may or potentially suffering a risk of hand arm vibration syndrome. The
preliminary results of free vibration analysis demonstrated that the grass trimmer experienced a
global first bending mode for 1st natural frequency, a global second bending mode for 2nd natural
frequency, a local first torsion mode for third natural frequency, and a combination of global and
local bending mode for 4th natural frequency. Later, the analyses were further carried out on the
modification of the grass trimmer.
Introduction
Grass trimmer, in which extensively been utilized as an agriculture machine for cutting the grass
has just about the same appearance since the model created 30 years ago. This indicates that the
evolution of this machine structure is still moderate and steady along the years [1,2]. Figure 1(a)
shows a hand-held grass trimmer model which commonly used in Malaysia.
Fig. 1. (a) Actual model and (b) Design model of grass trimmer
Since 10 years ago, many researchers have involved in the grass trimming technology and
development. These days, the current pattern in grass trimmer design involves the reduction of
costs, and easy for carrying [3]. The pursuit of these goals results in lighter grass trimmer, which
uses less and lighter materials. However, the result of lighter grass trimmer leads to higher vibration
as well as structural resonance within the range of forcing frequency [4,5]; which originating from
the motor and rotating blade. Therefore, within the frequency range, grass trimmer will have a
tendency to vibrate excessively, in which later affect the operator discomfort. In addition, a long
term exposure may cause operator having the hand-arm vibration syndrome—defined as a vibration
transmitted to the hand and arm during the operation of hand-guided equipment [6‒8].
This is why the study on structural modes or also known as dynamic behaviour of a machine is
considered important as all structures including grass trimmer have natural modes which often
create excessive vibration levels and premature failures if excited [9‒11]. Each structural mode is
characterized by its natural frequency and mode shape. At or near a natural frequency, the operating
deflection shape of a structure is usually dominated by a mode.
This paper focuses on determining the dynamic characteristics of grass trimmer by using finite
element method (FEM). The FEM was adopted in this study because of the effectiveness and
easiness to be implemented by just using a computer [11]. It divides the model into a simple model
form known as elements and can effectively solve many problems of analysis. In this case, a free
vibration analysis was employed to determine the natural frequency and mode shape of grass
trimmer. In the free vibration analysis, only initial load but no external force acts on the system and
the system is left to vibrate on its own.
Mathematical Equations
To obtain poles and frequencies from the finite element model, an eigensolution is performed on the
mass and stiffness matrices. The equation of motion for a multiple degree of freedom system is
written in matrix form as [10]:
M x Cx  K x  F t 
(1)
where [M] is mass matrix, [C] is damping matrix, [K] is stiffness matrix, {F(t)} is forcing vector
and {x} is vector of displacements.
The so-called normal mode eigensolution is obtained using only the mass and stiffness matrix
and assumes that the damping is either zero or proportional.
K  M   0
(2)
The eigensolution provides eigenvalues, λ which is also known as frequencies and eigenvectors,
φ which is also known as mode shapes.
Hand-Held Grass Trimmer
The model of hand-held grass trimmer that was studied is ECHO RM315SI. The specifications of
the grass trimmer are 30cc engine with 950 watt power and use metal blade to cut the grass. It is
one of common model used in Malaysia. Figure 1(a) displays the model of a grass trimmer used in
the current study.
Finite Element Modelling
In prior to FE analysis, Solidwork®―a mechanical design automation software was used to draw
the grass trimmer as illustrated in Figure 1(b), based on the exact dimensions of the hand-held grass
trimmer taken from the vibration laboratory, Universiti Tun Hussein Onn Malaysia. The model was
then later exported to Ansys®, and simulated using Ansys Workbench by fixing the constraint on
the grass trimmer's handle with moment force acts on a blade. However, in order to simplified the
FE analysis, the following consideration had been taken [11]: (i) all brackets, rubber connector from
rod to motor and the motor were excluded from the model, (ii) the connection of rod to handle and
blade were consider perfect, and (iii) the materials used for rod, handle and blade were considered
isotropic in its elastic phase.
Figure 2 shows the complete FE of grass trimmer model after meshing analysis. The 8-node
hexahedral element was chosen in the meshing analysis, which generates 8,193 nodes and 1,984
elements. Based on our previous finding [11,12], it was found that this element gave a closer result
to the actual condition. The model was fixed at grass trimmer handle with no load was assigned
since free vibration analysis was adopted in the study.
Fig. 2. FE meshing model of grass trimmer
Results and Discussion
The frequency range of interest used for the free vibration analysis was set between 10 to 1000 Hz.
The reason for setting the starting frequency at 10 Hz was to avoid the solver from calculating rigid
body motions which have the frequency of 0 Hz [11]. Under this study, only the next four
fundamental frequencies were observed, as these frequencies are critical to the grass trimmer
dynamic behaviour. Table 1 tabulates the first four natural frequencies obtained for the grass
trimmer model. Obviously, the natural frequency value increases as the number of modes increase.
Table 1. Natural frequency of grass trimmer
Mode (nth)
Frequency (Hz)
1
17.8
2
117.2
3
337.4
4
664.2
Figures 3 until 6 represent typical mode shape of the grass trimmer at 17.8, 117.2, 337.4 and
664.2 Hz, which corresponding to first, second, third and fourth natural frequencies, respectively.
The contour shows the translation value of the grass trimmer in x-, y-, and z-axes under vibration
modes. Noting that the translation value is unitless or without any unit since no force is applied in
free vibration analysis.
As seen in Figure 3, the first mode shape experienced by the grass trimmer is a global first
bending mode. Meanwhile, the second mode shape of grass trimmer indicates a global second
bending mode as shown in Fig. 4.
In contrast to first and second modes, the third mode of grass trimmer as displayed in Fig. 5
shows that the grass trimmer experiences a local first torsion mode which occurred at the cutter
blade. This obviously indicates that cutter blade will vibrate excessively in torsional shape when the
grass trimmer is excited at 337.4 Hz. Fig. 6 displays the grass trimmer experiences a combination of
global and local third bending mode, which obviously seen occur at the rod and cutter blade.
Fig. 3. FEA first mode shape @ 17.8 Hz
Fig. 4. FEA second mode shape @ 117.2 Hz
Fig. 5. FEA third mode shape @ 337.4 Hz
Fig. 6. FEA fourth mode shape @ 664.2 Hz
Conclusion
A finite element model of grass trimmer was developed to determine its dynamic behaviours such
as natural frequency and mode shape using free vibration approach. The research study reveals
more understanding on the grass trimmer's natural frequency and the mode shape characteristics,
where local and global vibration were found in the vibration modes of grass trimmer. In later stage,
a further modification will be performed to improve the grass trimmer's dynamic behaviour as well
to reduce the vibration level experienced by grass trimmer.
Acknowledgement
IZ thanks Office for Research, Innovation, Commercialization and Consultancy Management and
Universiti Tun Hussein Onn Malaysia for the financial support and provide facilities for this
research.
References
[1] Y.H. Ko, O.L. Ean, Z.M. Ripin, The design and development of suspended handles for reducing
hand-arm vibration in petrol driven grass trimmer, International Journal of Industrial Ergonomics
41 (2011) 459-470.
[2] Y.H. Ko, L.X. Mei, Z.M. Ripin, Tuned vibration absorber for suppression of hand-arm vibration
in electric grass trimmer, International Journal of Industrial Ergonomics 41 (2011) 494-508.
[3] Z. Mallick, Optimization of the operating parameters of a grass trimming machine, Applied
Ergonomics 41 (2010) 260-265.
[4] I. Zaman, A. Khalid, B. Manshoor, S. Araby, M.I. Ghazali, The effects of bolted joints on
dynamic response of structures, IOP Conference Series: Materials Science and Engineering 50
(2013) 012018.
[5] I. Zaman, M.M. Salleh, B. Manshoor, A. Khalid, S. Araby, The application of multiple vibration
neutralizers for vibration control in aircraft, Applied Mechanics and Materials 629 (2014) 191-196.
[6] M. Bovenzi, Exposure-response relationship in the hand-arm vibration syndrome: an overview
of current epidemiology research, International Archives of Occupational and Environmental
Health 71 (1998) 509-519.
[7] Y. Musson, A. Burdorf, D.V. Drimmelen, Exposure to shock and vibration and symptoms in
workers using impact power tools, The Annals of Occupational Hygiene 33 (1989) 85-96.
[8] A.H. Tudor, Hand-arm vibration: product design principles, Journal of Safety Research 27
(1996) 157-162.
[9] I.Z. Bujang, M.K. Awang, A.E. Ismail. Study on the dynamic characteristic of coconut fibre
reinforced composites. in Regional Conference on Engineering Mathematics, Mechanics,
Manufacturing & Architecture (EM3ARC), 2007, Putrajaya, Malaysia.
[10] C.R. Fuller, S.J. Elliott, Active control of noise and vibration, Academic Press, London, 1996.
[11] I. Zaman, R.A. Rahman, H. Khalid, Dynamic analysis on off-road vechicle chassis using 3-d
finite element model, Journal of Science and Technology 4 (2007) 1-16.
[12] I. Zaman, M.M. Salleh, M. Ismon, B. Manshoor, A. Khalid, M.S.M. Sani, S. Araby, Study of
passive vibration absorbers attached on beam structure, Applied Mechanics and Materials 660
(2014) 511-515.