Analysis of mechanical structure under vibration using vibration

INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 1, January- February (2013), pp. 134-141
IJMET
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ANALYSIS OF MECHANICAL STRUCTURE UNDER VIBRATION
USING VIBRATION MEASURING SYSTEM

R S Rajpurohit1, R S Prasad2
1
Assistant Professor, Department of Mechanical Engineering, ABESEC, Ghaziabad, INDIA
2
Professor, Department of Mechanical Engineering, RKGIT, Ghaziabad, INDIA

ABSTRACT

Vibration is useful in order to realise system alive but beyond a particular value,
vibration becomes dangerous for the existence of the system. In the present investigation
effort has been made to fabricate and develop a mechanical structure along with a measuring
system so that when structure vibrates, behaviour of vibrating structure can be monitored at
various frequency of vibration. In order to simplify the fabrication work, the experimental
setup was categorized into two, as mechanical structure system and vibration measuring
system. Mechanical structure system was further subdivided into three different mechanical
systems as, (1) mechanical vibrator, (2) vibration transformation mechanism, and (3)
mechanical structure. Dimensions of mechanical vibrator, vibration transformation
mechanism and mechanical structure were taken in order to suit the requirement of
experimental work. Drawings of structure were developed using AutoCAD for better analysis
prior to the fabrication work. As per the drawings, the setup was fabricated using materials,
mild steel and aluminium. Potentiometers were used to develop vibration measuring system.
The mechanical vibrating system simulates the real vibrating structures and the measuring
system records the linear displacement of sensors. In a combination the linear displacement
of the sensors indicates mode-I of vibration and for other set of displacement of sensors it
indicates mode-II of vibration. The frequency of vibration in each case was observed using
tachometer. Using FEM package (ABACUS) the vibrating system was again simulated in
order to compare the behaviour and outcomes.

Keywords: Mode-I, Vibrating Structure, Potentiometer, Vibrator.

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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

INTRODUCTION

Vibration is an integral part of any existing live system. Sometimes vibration is
desirable and sometimes not. All machines in working condition vibrate and part of input
energy dissipates through vibration and part of energy gets transformed into useful work.
Efficiency of the system deteriorates with increase in vibration of system through which there
is an energy loss. In order to know unwanted vibration we need to monitor vibrating system.
This took attention for investigation and therefore decided to develop a system which can be
used to measure vibration of any system vibrating. A structure can be defined as a
combination of parts fastened together to create a supporting framework, which may be part
of a building, machine, and any other mechanical system. Before the Industrial Revolution
started, structures usually had a very large mass because heavy timbers, castings and
stonework were used in their fabrication; also the vibration excitation sources were small in
magnitude so that the dynamic response of structures was extremely low. Furthermore, these
constructional methods usually produced a structure with very high inherent damping, which
also gave a low structural response to dynamic excitation. The vibration that occurs in most
machines, structures and dynamic systems is undesirable, not only because of the resulting
unpleasant motions, the noise and the dynamic stresses which may lead to fatigue and failure
of the structure or machine, but also because of the energy losses and the reduction in
performance that accompany the vibrations. It is therefore essential to carry out a vibration
analysis of the proposed structure.

LITERATURE REVIEW

The concept of employing structural control to minimize structural vibration was
proposed in the 1970’s [1]. It was proposed that for un-damped linear systems, equations of
motion can be given by mü(t) + ku(t) = F(t) [2]. Also, it has been observed that, any
mathematical damping model does not give a detailed explanation of the underlying physics
[3]. Several mathematical models of physical damping mechanisms in single degree of
freedom systems were developed [4]. Banks and Inman have considered four different
damping models for a composite beam [5]. This damping behaviour has been studied by
many authors [6] in some practical situations. It was recognized that the energy dissipation in
a lap joint over a cycle under different clamping pressure is possible [7]. Significant damping
can be obtained by suitably choosing the fastening pressure at the interfacial slip in joints [8].
Forced vibration conditions for structural analysis of the systems have been developed as one
means in order to minimize the effect of environmental loads [9, 10]. Warburton and Soni
have suggested a criterion for such a diagonalization so that the computed response is
acceptable [11]. Using the frequency domain approach, Hasselsman proposed a criterion for
determining whether the equations of motion might be considered practically decoupled if
non-classical damping exists [12]. In order to achieve better protection against vibration even
helical springs are used as shock absorbers with fluid dampers as energy dissipaters [13].
Sung Joon Kim and In Hee Hwang worked on the topic, ‘Prediction of fatigue damage for
composite laminate using impact response’ and found that an impact response model can be
used to compute the fatigue damage [14]. Damage such as an adhesive disband and fatigue
damage results in a decrease in structural stiffness, and hence a change in the nature of
impact [15]. Adams showed that it is possible to produce a version of the coin-tap test which
depends on the measurement of the force input to the test structure during the tap, rather than

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on the measurement of the sound produced by the tap [16]. A.N. Damir, A. Elkhatib and G.
Nassef worked on the topic, ‘Prediction of fatigue life using modal analysis for grey and
ductile cast iron’ to investigate the capability of experimental modal analysis, as a non-
destructive tool, to characterize and quantify fatigue behaviour of materials [17]. The modal
parameters are, by definition, functions of the physical properties of components (i.e. mass,
stiffness or modulus of elasticity) and hence of mechanical properties. This concept was used
mainly in the application of modal testing as an acceptance test for castings [18, 19]. The
influence of geometric imperfections on the natural frequencies of cylindrical shells was
studied [20, 21], and later also their influence on the non-linear vibrations [22, 23]. The
effects of boundary conditions and static axial compressive loading on the non-linear
vibrations were also investigated [22]. In recent past, a strong interest for the non-linear
elastic wave spectroscopy methods applied to non-destructive testing has grown [24].
Different studies of this behaviour have been applied on a large range of materials: harmonic
analysis [25], parametric interactions [26], modulation of amplitude [27] and phase [28] and
studies of resonance frequency [29, 30]. Mathematical modelling is instrumental in the
ongoing optimization of multi-layer designs and characterization techniques for
multifunctional hybrid systems and composite structures [31, 32]. The multiple layers of
single-purpose materials are replaced in various structures by their multipurpose counterparts.
The full advantage of hybrid composites can be realized only when the micro-structural
damage is controlled during processing [33], service and repairs.
THEORETICAL WORK
It was realised that, in order to observe the effect of damper on the vibration
transmitted to the structure, a system has to be developed so that frequency of vibration can
be recorded for a particular vibration signature. Here, mode of vibration was found adequate
and convenient to observe. Therefore, initially a system was developed using AutoCAD
constituting of, a vibrator, vibration transformation system and a structure. Three boxes were
joined together using flexible joints to act as a structure. A vibration transformation system
was developed so that vibration can be transformed from vibrator to structure in a particular
order. Three different vibration transformation systems were developed, each to establish a
new experimental condition. The difference between the three was their ability to absorb
vibration. A simple mechanical vibrator was also developed as a source of vibration. The
need of structure was only to develop a mechanical system to simulate vibration. The idea of
structure was initiated from the analysis work done in the previous research work, and was
shaped just to fulfil the requirement of experimental work. A vibration measuring system was
also developed to record the modes of vibration and frequency when mode-I and mode-II of
vibrations are attained.
DEVELOPMENT OF STRUCTURE USING AUTOCAD
With the extensive use of software (AutoCAD) the mechanical structure system was
developed as shown in the Fig.4. Mechanical vibrator, vibration transformation mechanism,
and mechanical structure were also drawn individually to have better understanding of each
part to be fabricated. Drawing of mechanical vibrator is as shown in Fig.1, drawing of
vibration transformation system is as shown in Fig.2 and drawing of structure is as shown in
Fig.3. Recognition of components of vibration measuring system becomes an important part
of research work. Vibration measuring system was a method developed to observe modes of
vibration of a vibrating structure.

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Fig.1: Mechanical Vibrator

Fig.2: Mechanism

Fig.4: Setup of Mechanical
Structure under Vibration

Fig.3: Structure

ELECTRONIC MEASURING SYSTEM
A microcontroller often serves as the “brain” of a mechatronic system. Here, a mini, self-
contained computer was designed and programmed to interact with both the hardware of the system
and the user. The most basic microcontroller was used to perform simple math operations, control
digital outputs, and monitor digital inputs. Potentiometers were used to observe the linear
displacement of the spring in order to establish method to record mode-I and mode-II of vibration.

EXPERIMENTAL WORK
A set up was fabricated in order to analyse the vibration affecting the structure and to observe
the usefulness of the vibration measuring system designed and developed in order to measure
frequency of vibration. Experimental work covers FEM analysis, fabrication of structure, fabrication
of vibration transformation mechanism, mechanical vibrator and vibration measuring system.

FEM ANALYSIS
With the extensive use of FEM package (ABACUS) the mechanical viability of the vibrating
system was checked by applying different constraints and material condition. Fig.5 describes the
deflection of structure at mode-I of vibration.

MATERIAL SELECTION
Using software package it was easy to understand the behaviour of vibrating structure. In
order to simplify the construction of complete system the materials were selected accordingly. For
structure boxes aluminium was selected. Springs were used to make the joints flexible and the
material of spring taken was spring steel. The nuts and bolts used to support the flexible joints and
were made of mild steel. The parts of vibration transformation system and vibrator system were
fabricated using mild steel plates.

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FABRICATION WORK

Boxes were developed with the extensive use of sheet metal work. Three boxes were made and then
assembled together. Vibration transformation mechanism system and mechanical vibrator system was fabricated
in workshop. The arrangement of cam & follower system was attached to DC motor with regulator in order to
control the rpm of motor and in turn vibration. The mechanical vibrator system is as shown in the Fig.6
A vibration transmitting mechanism is then attached with the mechanical vibrator to achieve the vibration on the
top plate on which the structure was fixed. Aluminium structure was then fixed over the plate so that the effect
of vibration can be observed. By adjusting the motor speed (rpm) frequency of vibration was to be adjusted.
To observe the modes of vibration the electronic measuring system was positioned and fixed to the structure as
shown in the Fig.7. The readings were observed on the display attached to the system and was governed by four
displacement sensors. All the four displacement sensors were fixed, two on the right side and two on the left
side in between the flexible joints of two boxes. Experimental work was done to observe the frequency of
vibration at Mode-I and Mode-II of vibration for the system and was tabulated. Readings were taken for the
three different vibration transformation mechanism systems and used for further analysis.

Fig.5: Structure at mode-I of vibration

Fig.6: Vibration system

Fig.7: Structure with
displacement sensors

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RESULTS AND DISCUSSIONS

From the tabulated data obtained from the experimental work it was observed that the
value of frequency was different as the vibration transformation mechanism changes. The
frequency of vibration at mode-I of vibration was 1.7 Hz and the frequency of vibration at
mode-II was 2.55 Hz when first vibration transformation mechanism was used.
The mechanism was modified by providing spring support both sides between the fixed plate
and the supported plate in order to change the damping capacity of the structure. The second
vibration mechanism used for experimental work and the frequency of vibration at mode-I of
vibration was 5.3 Hz and the frequency of vibration at mode-II was 9.1 Hz. The mechanism
was further modified by providing bolt and a spring support to make a flexible joint at one
end between the fixed plate and the supported plate in order to set a different damping
capacity of the structure. The third vibration mechanism was used for experimental work and
the frequency of vibration at mode-I of vibration observed was 7.12 Hz and at mode-II it was
13.28 Hz. The value of frequency observed for each vibration transformation mechanism at
mode-I and at mode-II of vibration was plotted as shown in Fig.8

Fig.8: Variation in the frequency with
the change in mechanism

CONCLUSIONS

It was found that the vibration transformation mechanism plays a vital role in
achieving modes of vibration. While performing experimental work the only change made in
the experimental setup was the vibration transformation mechanism, as a result of which the
frequency for the modes of vibration changes. It was observed that as the damping capacity
of vibration transformation mechanism increases the frequency for the modes of vibration
increases as shown in the Fig.8. No remarkable change was observed in the maximum
deflection of the structure at mode-I of vibration. Therefore it can be concluded that as the
damping capacity of vibration transformation mechanism increases the structures are safe and
mode-I and mode-II of vibration attained will be observed at higher frequency of vibration.

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