DYNAMICAL ANALYSIS OF SILO SURFACE CLEANING ROBOT USING FINITE ELEMENT METHOD

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 7, Issue 1, Jan-Feb 2016, pp. 190-202, Article ID: IJMET_07_01_020
Available online at
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ISSN Print: 0976-6340 and ISSN Online: 0976-6359
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DYNAMICAL ANALYSIS OF SILO
SURFACE CLEANING ROBOT USING
FINITE ELEMENT METHOD
Kinan. Dandan, Anani. Ananiev, Ivan. Kalaykov
School of Science and Technology, Örebro University, 70182 Örebro, Sweden
ABSTRACT
All mechanical systems are subjected to dynamic forces when they are in
functioning. Thus a dynamical analysis has to be studied to determine the
system behaviour. The vibration is of interest to study, due to its destructive or
constructive effect. In the present era computational techniques are quite
common and are very reliable as far as the modal analysis is concerned. In
this work, the robot of silo cleaning is analysed for its vibration behaviour
using finite element method (FEM).The robot was modelled and meshed in
ANSYS. Modal analysis was conducted to calculate few initial natural
frequencies. After carrying out the modal analysis, harmonic and transient
analysis were done to see the response of the robot under dynamic loading. It
was observed that robot is safe in its entire range of operation.
Key words: Silo, Suspended Robot, Finite Element, Modal Analysis,
Dynamic Analysis.
Cite this Article: Kinan. Dandan, Anani. Ananiev, Ivan. Kalaykov.
Dynamical Analysis of Silo Surface Cleaning Robot Using Finite Element
Method, International Journal of Mechanical Engineering and Technology,
7(1), 2016, pp. 190-202.
http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=7&IType=1
1. INTRODUCTION
The increasing demands of safety and reliability on mechanical systems have
improved the scientific understanding of dynamic properties of structure. All real
physical structures behave dynamically when subjected to loads or displacements
which varies with time. In such cases, a dynamic analysis is applied to reflect both the
varying load and response, where the vibrations of a structure is of interest. Vibrations
can be destructive and should be avoided, or they can be extremely useful and desired.
If the loads or displacements are applied very slowly (the frequency of loading is less
than one third of the lowest natural frequency of the structure), the inertia forces can
be neglected and a static load analysis can be justified.

Dynamical Analysis of Silo Surface Cleaning Robot Using Finite Element Method
The dynamic analysis of a mechanical structure consists of three steps: defining
the analytical model (continuous or lumped-mass model), deriving the mathematical
model by applying the physical laws, and solving the equations of motion to have the
dynamical response [1]. Many dynamics problems cannot be solved by lumped
parameter models as a more accurate modelling of the distributed elastic behaviour of
the structure is needed. Structures with complex geometry, material properties or
boundary conditions, are modelled using numerical methods that provide approximate
but acceptable solutions. The finite element modelling (FEM) is one of the most
powerful and popular mathematical modelling techniques.
In a previous work [2], a concept of a suspended robot for surface cleaning in silos
(SIRO) was presented (Fig.1). The suggested design appears to be a reasonable
compromise between the basic contradicting factors, small entrance and large surface
of the confined space. It contains:
 Cleaning robot with two platforms - in retracted form on Fig.1(a) and in opened form
on Fig.1(b). Each platform consists of central body and three telescopic arms;
 support unit consisting of: control unit for all functions of the system; lifting arm for
positioning the cleaning robot at the silo central axis and spools unit contains spool of
steel cables with respective driving motors used for robot suspension and motion;
 Cleaning tools attached to the centre of the platform which rotate around the platform
centre, i.e. around the silo vertical axis.
Figure 1The proposed SIRO cleaning robot inside a silo
In operation, the cleaning tool removes the build up materials from the inside silo
surface by blowing a pressurised air on a stripe while rotating around the silo vertical
axis, and the robot fully covers the inner surface of the silo through successive
crawling movements of its two platforms. During these two essential process
(cleaning and crawling), the system is subjected to different types of loads, hence a
dynamic analysis for system is required to predict its response.
(a) The initial pose (b) The working pose

The main purpose of this study is to calculate the dynamic characteristic of the
robot i.e. the natural frequency and the mode shapes by using modal analysis method.
The dynamic characteristics are computed by the finite element analysis software
(ANSYS). The information provided by modal analysis is used to understand the
behaviour of the structure under general excitation. Thus verifying whether or not the
robot will successfully overcome resonance, fatigue, and other harmful effects of
forced vibrations.[3, 4].
The paper is organized as follows: Section 2 describes the finite element model of
SIRO. Then, in Section 3 the static structure analysis is presented. Section 4 discusses
the dynamic analysis of SIRO through applying the most common types of analyses:
modal, harmonic frequency response, and transient dynamic analysis. Finally section
5 provides some conclusions of this work.
2. FEM OF ROBOT STRUCTURE
The three-dimensional solid model assembly of the robot with silo and silo roof in
opened form was built in CAD software and imported to ANSYS Workbench by
direct interface ( figure 2). the robot consists of cable, two platforms with three arms
for each, three linear shafts installed between the two platforms, and the cleaning tool
with the end effector. The cable is modelled as a set of bonded segments (25
segments) where the first segment is fixed to the silo dome and the last one is fixed to
the top platform.
Figure 2 The system model in Ansys environment, the silo is hidden
After the model is imported, the type of material is assigned for each part. Three
materials are defined for the model: the silo and its roof are concrete, the cable and
the three linear shafts are steel and the platforms with the arms are aluminium alloy.
the material proprieties are well defined in the ANSYS.
ANSYS Workbench automatically recognizes the contacts existing between each
part. The contact conditions for corresponding contact surfaces and the joints between
parts are defined. Frictionless contact type was chosen as contact condition for contact
surfaces between the arms and the platforms’ shoulders. The contact surfaces arms-
silo have friction contact type with friction coefficient value of 0.6. The rest of contact
surfaces have a completely bonded contact type. Rotation joints are defined between
the arms and the platforms.
The model is meshed automatically with suitable meshing elements, the default
element size is determined based on a number of factors including the overall model
size, the proximity of other topologies, body curvature, and the complexity of the
feature. The model parts are meshed using higher order 3D solid elements; SOLID186

defined by 20 nodes and SOLID187 defined by 10 nodes. Both elements have
quadratic displacement behaviour, and have three degrees of freedom per node:
translations in the nodal x, y, and z directions. SOLID187 is well suited to modelling
irregular meshes such as those produced from various CAD/CAM systems [5]. The 25
segments of the cable and the three linear shafts are meshed with SOLID186, where
they have a regular shape, while the other parts meshed with SOLID187.
For modelling the contact surfaces, CONTA174 and TARGE170 elements were
used. CONTA174 element was located on the surfaces of 3- D solid elements
SOLID186 and SOLID187. TARGE170 is used to represent various 3-D “target”
surfaces for the associated contact element CONTA174, which has the same
geometric characteristics as the solid or shell element face with which it is connected.
Contact occurs when the element surface penetrates one of the target segment
elements (TARGE170) on a specified target surface. Coulomb friction, and shear
stress friction are allowed. A contact sizing meshing is applied on the contact surfaces
arms-silo to refine the calculation [5].
The model will be analysed statically and dynamically when the arms have
friction/frictionless contact with the silo. The friction contacts are occurred by the
internal forces (Finternal) that are applied through the telescopic arms. While in the
absence of these forces the contacts arms-silo will be frictionless.
3. STATIC STRUCTURAL ANALYSIS
A static structural analysis determines the displacements, stresses, strains, and forces
in structures or components caused by loads. The loads consist of boundary
conditions as well as internally and externally applied forces. The gravity force (B in
the figure 2) and the fixed support , silo and its roof, (A in the figure 2) are defined in
all simulation tests.
The simulations are done for two different loads, with/without Finternal (C-F in the
figure2). Figure 3(a) shows the pressure on the contact surfaces when Finternal are
applied, the maximum pressure is noticed on arms-silo contact surfaces. Thus
adequate friction forces arise on the contact surfaces arms-silo and achieve an
appropriate stability to the system. While in figure 3(b), where there is no Finternal, the
pressure on these surfaces is almost zero.
Figure 3 Pressure on contact surfaces when there are a) internal forces. b) no internal forces
(a)
Maximum pressure on the contact surface
arms-silo (b) Maximum pressure on the contact
surface arm platform

Figure 4 The total deformation when there are a) internal forces. b) no internal forces
Therefore comparing the deformation of the robot with(fig 4(a)) / without (fig
4(b)) the effect of applying the internal forces shows that in the first situation the
telescopic arms of the robot bend on the level of the second segments of the arms
indicating that the arms have fix points on silo surface. While in the second situation
the arms have the maximum deflection at the distal end of the arm which indicate that
the arms have a free end. The maximum deformation of the robot with/without
internal forces is placed on the distal ends of the cleaning tool and it is in the range of
16 mm, which is an acceptable deformation regarding to the length of the cleaning
tools (3.5m for each arm).
The equivalent Von Mises stress analysis of the system (fig. 5) shows that the
maximum stress (with Finternal ) is located on the contact surface arms-silo ( 58 MPa ).
It is less than the yield point value of the arm material. In the other case (without
Finternal) the maximum value of stress is at the connection arm-platform and it is in the
safety range too (22 MPa). So the design is statically safe.
Figure 5 The equivalent stress (Von Mises) when there are a) internal forces. b) no internal
forces
(a) With internal force (b) No internal force
(a) The arms deformation are at the middle
of the arms
(b) The arms deformation are at end of the
arms

4. DYNAMIC ANALYSIS
The dynamic analysis attempts to solve the motion equations (1) of every node point
in the structure, which are determined in matrix form as
(1)
where, [M] represents the structural mass, the nodal acceleration vector, [C]
the structural damping matrix, the node velocity vector, [K] the structure stiffness
matrix, {X} the node displacement vector and {F} is the applied time varying force
vector. This equation is a set of differential equations for the dynamic response of a
structure modelled with a finite number of degrees of freedom. Finite element
analysis as a computer modelling approach has provided engineers with a flexible
design tool, especially when dynamic properties need to be perused. The following
categories of dynamic analysis may be classified [6]:
Modal analysis: This is the first step required before performing any other type of
dynamic analysis and will determine the dynamic characteristics of a system in terms
of the natural frequencies and mode shapes of the structure. One objective of this
analysis is to make sure that the structure is not operating at a frequency close to one
of its natural frequencies. With respect to the mode shapes, it is desirable to avoid
mode shapes that are similar to deformation patterns obtained from the static loading
on the structure.
Frequency response analysis: This type of analysis is performed if the loading on
the structure is harmonic or periodic. The displacements, velocities, and accelerations
are the output of such analysis. Assuming linear conditions, the response to multiple
frequency inputs may be simply summed up using the superposition technique.
Transient response analysis: This type of analysis is performed if the loading on
the structure is classified as transient or shock. The output of transient analysis is time
histories of displacements, velocities, and accelerations of the system that may be
used to calculate forces and stresses.
4.1. Modal analysis
The concept of modal analysis is that the natural modes of vibration express the
vibration response of a linear time-invariant dynamic system. The natural modes of
vibration are determined by the physical properties ( mass, stiffness, damping) and the
boundary conditions of the dynamic system. Each mode is expressed in terms of its
modal parameters: natural frequency, modal damping factor and mode shape [7].
The natural frequencies of the system may be obtained by solving the eigenvalue
problem which derives from the general equation (1) by zeroing the damping and
applied force terms:
(2)
where the eigenvalue is w2, and {A} is the eigenvector associated with each value
of w2. The total number of eigenvalues or natural frequencies is equal to the total
number of degrees of freedom in the model. Since each of the eigenvectors cannot be
null vectors, the equation which must be solved, let λ = w2, is
([K] − λ[M]) = {0} (3)
Necessary and sufficient condition for the equation (3) to have non-zero solution
is that determinant of ([K] − λ [M]) is zero.

By modal analysis techniques, a large and complex system can be divided into
several subsystems which can be independently analysed, thus the dynamic
characteristics of the overall system can be determined from the subsystem
information, and the design of a complex system can be carried out by designing and
developing its subsystems separately [7]. Our system can be decomposed to three
subsystems: two platforms with cables and the cleaning tool. In this paper, only the
dynamic analysis of the platform with the cable is studied.
Two modal analysis are studied to the platform with cable: first when the arms of
the platform have fixed supports (the internal forces through the arms produce friction
force in the contact surface arms-silo). The second when the arms have free ends (the
complete model has no internal forces through the arms). In the two studies the free
end of the cable is supposed fix support.
Table 1 compare the first thirty natural frequencies fw of the system with internal
forces and those fwout when there are no forces. It is clearly noticed that there are
difference in the natural frequencies. There is only one identical frequency (58.103
Hz), and the mode shapes (Fig.6) corresponding this frequency show an oscillation to
the cable in both when the arms are free and fixed.
Table 1 The first thirty natural frequency of the system with/without internal forces through
the telescopic arms
mode fwout Hz fw Hz mode fwout Hz fw Hz mode fwout Hz fw Hz
1 0.18686 10.229 11 22.224 49.294 21 64.225 105.31
2 0.38422 10.246 12 22.312 51.398 22 67.221 112.29
3 0.38429 11.128 13 24.603 51.64 23 67.488 112.38
4 1.4572 11.138 14 29.723 58.103 24 73.525 113.8
5 1.4604 11.766 15 29.736 58.127 25 81.202 141.13
6 10.074 22.137 16 31.665 60.3 26 81.427 141.15
7 10.1 22.179 17 36.804 64.922 27 95.986 146.07
8 10.105 22.403 18 36.865 65.001 28 96.028 146.14
9 10.914 29.622 19 58.078 95.831 29 102.58 163.51
10 10.919 29.636 20 58.103 95.873 30 123.13 168.41
Figure 6 Mode shape of identical natural frequency of the platform; free arms (left), fixed
arms (right)

Figure 7 Mode shape of the first natural frequency for the platform; free arms (left), fixed
arms ( right )
Figure 7 shows the mode shape of the model at the first natural frequency when
the distal ends of arms are free and fixed. The first mode with free arms shows a
rotation to the platform on the axis Z. While when the arms have fixed ends, there is a
torsion of the platform and two arms around the axis of the third arm.
Figures 8and 9 present different mode shapes of the platform when the distal ends
of arms are free and fixed respectively. Mode 27 (free arms)and mode 19 (fixed arms)
have the same behaviour due to having almost the same natural frequencies.
Figure 8 Mode shape of different natural frequencies for the platform (free arms)

Figure 9 Mode shape of different natural frequencies for the platform (fixed arms)
4.2 Harmonic frequency response
Frequency response analysis (FR) is a method used to compute the steady state
response of a structure to an oscillation excitation. Harmonic excitation are very
common source of external force applied to structures. In addition, the Fourier
theorem indicates that many non-harmonic forcing functions can be expressed as an
infinite series of harmonic terms. By using the principle of superposition, the total
response is represented as the sum of the response to the individual terms. The forcing
function can be defined as:
{F} = {F0}eiwt
(4)
where F0 is the peak force amplitude and w is the harmonic frequency.
The nodal displacement therefore has the form
{X} = {X0}eiwt
(5)
Substituting (5) in the general equations of motion (1) results in
(6)
which shows that the displacement,{X0} is a function of frequency, damping and
force amplitudes. Solving this equation (6) over a discrete range of frequency inputs
determines the vibration frequency response.

Figure 10 Frequency response of the platform
Figures 10,11 and 12 present the frequency response of the platform , the second
segment of the arm and the distal end of the arm respectively, when the arms are fixed
and free. The harmonic force is applied on the platform in Z direction where the
frequency range is between 0 to 200 Hz and the the peak force amplitude F0 = 1000N.
From the previous figures we can notice that the model start responding when f =
10Hz for free arms and 22.5Hz for fixed arms. Also it is noticed that when the arms
have fixed ends the dominant frequency is 163.5Hz, while it is 73.5Hz when the arms
have free ends.
Figure 11 Frequency response of the second segment of the arm

Figure 12 Frequency response of the distal end of the arm
From this analysis, we can conclude that the frequency of the harmonic excitation
should be less than 10 Hz to not have any significant response of the platform. In
another words, the rotation of the cleaning tool should not be bigger than 600 rpm.
4.3. Transient response
This type of analysis is used to determine the time-varying displacements, strains and
stresses in a structure as it responds to a transient load. There are two basic
approaches to transient analysis. The first involves solving the systems of equations
by direct integration which involves the whole systems of equations and requires
many time steps with a complete solution in each step. This can become a large
computing task for moderate sized problems. The second approach is known as modal
superposition which assumes that the response of the structure can be adequately
represented by the lower natural frequencies of the structure. The complete response
therefore, is the summation of the correct fractions of the low frequency mode shapes.
Mathematically, this involves a transformation of the equation from nodal
displacement co-ordinates into a set of modal co-ordinates. This results in much fewer
equations, but results in an approximate solution being obtained. However, this has
proven to be sufficiently adequate for most structural vibration problems [6]. The
transient load is modelled as transient force applied on the platform in the Z direction.
This force represents the effect of the acceleration of the second platform when it
starts the crawling movement and before it becomes uniform motion along the linear
shafts between the two platforms. The force F is applied on the platform in 0.002
second at the moment 0.02; the maximum value 10000 N is reached after 0.001
second.

Figure 13 Stress transient response of 2nd arm’s segment when applying shock force in the Z
direction
Figures 13 and 14 show the stress and deformation of the second segment of the
arm on the Z direction respectively, when the arms have free / fixed ends. Von Mises
stresses obtained from finite element analyses are utilized in fatigue life calculations.
All fatigue analyses are performed according to infinite life criteria (i.e., N = 109
cycles). Comparing the safety factor of the second segment of the arm in static (Sfactor
= 15) and dynamic analysis (Sfactor = 9.7) indicates that the arm predicted to be safe
against fatigue under static and dynamic loadings.
Figure 14 Deformation transient response of 2nd arm’s segment when applying shock force
in the Z direction
5. CONCLUSION
The aim of this study was to determine the static and dynamic finite element analysis
of SIRO by using ANSYS. The static structural analysis is implemented to SIRO with
silo model in two different boundary conditions: first when there is a friction contact
on the contact surface arms-silo, thus the arms are considered having fixed contact
with silo, second when there is no friction contact therefore the arms have free ends.
The dynamic analysis is conducted by applying modal analysis, harmonic frequency
response and transient response. Depending on the properties of modal analysis, the
dynamic analysis in this study is implemented on the subsystem of SIRO, which
consists of platform, three arms and cable. Using the eigenvalues and eigenvectors
from the modal analysis, a harmonic response and a transient response to the
subsystem is carried out indicating that the subsystem is safe under the dynamic
loading.

Future work: The limitations of the FEM approach lie in the increasing model size
required to properly describe complex structures with appropriate detail (models with
over 1 million degrees of freedom are used today in the car and aircraft industry). This
leads to higher model construction and calculation times, but even more important,
there remain inherent modelling accuracy limitations, related to the modelling of
structural junctions, non-homogeneous elements, complex materials etc. [8] To
address these limitations, an experimental approach to modal analysis must developed
yielding results which can be used either as a model by itself, or to validate and
improve the FE models.
REFERENCES
[1] R. C. Roy and J. K. Andrew, Fundamentals of Structural dynamics. Jhon wiley
and Sons, 1st ed ed., 2006.
[2] Kinan Dandan, Anani Ananiev, Ivan Kalaykov, “Siro: The silos surface cleaning
robot concept,” in Mechatronics and Automation (ICMA), 2013 IEEE
International Conference on, pp. 657–661, 2013.
[3] J. He and Z.-F. Fu, “Overview of modal analysis,” Modal Analysis, pp. 1 – 11,
2001.
[4] D. J. Ewins, Modal testing: theory, practice, and application. Baldock,
Hertfordshire, England; Philadelphia, PA: Research Studies Press, 2 nd ed ed.,
2000. Previous ed.: 1995.
[5] ANSYS, “12.0,” ANSYS Theory Reference, 2009.
[6] M. S. Gadala, “Finite element applications indynamics,” Mechanical
Engineering Series, pp. 1–57, Jun 2005.
[7] C. de Silva, “Modal analysis,” Mechanical Engineering Series, pp. 1 –57, Jun
2005.
[8] H. Van der Auweraer, Structural dynamics modeling using modal analysis:
applications, trends and challenges, in Instrumentation and Measurement
Technology Conference, 2001. IMTC 2001. Proceedings of the 18th IEEE, vol. 3,
pp. 1502–1509, IEEE, 2001.

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