Analysis of mechanical structure under vibration using vibration

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  • 1. 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© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2012): 3.8071 (Calculated by GISI)www.jifactor.com ©IAEME 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. 134
  • 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEMEINTRODUCTION Vibration is an integral part of any existing live system. Sometimes vibration isdesirable and sometimes not. All machines in working condition vibrate and part of inputenergy 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 thereis 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 beused to measure vibration of any system vibrating. A structure can be defined as acombination of parts fastened together to create a supporting framework, which may be partof a building, machine, and any other mechanical system. Before the Industrial Revolutionstarted, structures usually had a very large mass because heavy timbers, castings andstonework were used in their fabrication; also the vibration excitation sources were small inmagnitude so that the dynamic response of structures was extremely low. Furthermore, theseconstructional methods usually produced a structure with very high inherent damping, whichalso gave a low structural response to dynamic excitation. The vibration that occurs in mostmachines, structures and dynamic systems is undesirable, not only because of the resultingunpleasant motions, the noise and the dynamic stresses which may lead to fatigue and failureof the structure or machine, but also because of the energy losses and the reduction inperformance that accompany the vibrations. It is therefore essential to carry out a vibrationanalysis of the proposed structure.LITERATURE REVIEW The concept of employing structural control to minimize structural vibration wasproposed in the 1970’s [1]. It was proposed that for un-damped linear systems, equations ofmotion can be given by mü(t) + ku(t) = F(t) [2]. Also, it has been observed that, anymathematical damping model does not give a detailed explanation of the underlying physics[3]. Several mathematical models of physical damping mechanisms in single degree offreedom systems were developed [4]. Banks and Inman have considered four differentdamping models for a composite beam [5]. This damping behaviour has been studied bymany authors [6] in some practical situations. It was recognized that the energy dissipation ina lap joint over a cycle under different clamping pressure is possible [7]. Significant dampingcan 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 onemeans in order to minimize the effect of environmental loads [9, 10]. Warburton and Sonihave suggested a criterion for such a diagonalization so that the computed response isacceptable [11]. Using the frequency domain approach, Hasselsman proposed a criterion fordetermining whether the equations of motion might be considered practically decoupled ifnon-classical damping exists [12]. In order to achieve better protection against vibration evenhelical 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 forcomposite laminate using impact response’ and found that an impact response model can beused to compute the fatigue damage [14]. Damage such as an adhesive disband and fatiguedamage results in a decrease in structural stiffness, and hence a change in the nature ofimpact [15]. Adams showed that it is possible to produce a version of the coin-tap test whichdepends on the measurement of the force input to the test structure during the tap, rather than 135
  • 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEMEon 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 andductile 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 modalparameters 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 usedmainly in the application of modal testing as an acceptance test for castings [18, 19]. Theinfluence of geometric imperfections on the natural frequencies of cylindrical shells wasstudied [20, 21], and later also their influence on the non-linear vibrations [22, 23]. Theeffects of boundary conditions and static axial compressive loading on the non-linearvibrations were also investigated [22]. In recent past, a strong interest for the non-linearelastic 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: harmonicanalysis [25], parametric interactions [26], modulation of amplitude [27] and phase [28] andstudies of resonance frequency [29, 30]. Mathematical modelling is instrumental in theongoing optimization of multi-layer designs and characterization techniques formultifunctional hybrid systems and composite structures [31, 32]. The multiple layers ofsingle-purpose materials are replaced in various structures by their multipurpose counterparts.The full advantage of hybrid composites can be realized only when the micro-structuraldamage is controlled during processing [33], service and repairs.THEORETICAL WORK It was realised that, in order to observe the effect of damper on the vibrationtransmitted to the structure, a system has to be developed so that frequency of vibration canbe recorded for a particular vibration signature. Here, mode of vibration was found adequateand convenient to observe. Therefore, initially a system was developed using AutoCADconstituting of, a vibrator, vibration transformation system and a structure. Three boxes werejoined together using flexible joints to act as a structure. A vibration transformation systemwas developed so that vibration can be transformed from vibrator to structure in a particularorder. Three different vibration transformation systems were developed, each to establish anew experimental condition. The difference between the three was their ability to absorbvibration. A simple mechanical vibrator was also developed as a source of vibration. Theneed of structure was only to develop a mechanical system to simulate vibration. The idea ofstructure was initiated from the analysis work done in the previous research work, and wasshaped just to fulfil the requirement of experimental work. A vibration measuring system wasalso developed to record the modes of vibration and frequency when mode-I and mode-II ofvibrations are attained.DEVELOPMENT OF STRUCTURE USING AUTOCAD With the extensive use of software (AutoCAD) the mechanical structure system wasdeveloped as shown in the Fig.4. Mechanical vibrator, vibration transformation mechanism,and mechanical structure were also drawn individually to have better understanding of eachpart to be fabricated. Drawing of mechanical vibrator is as shown in Fig.1, drawing ofvibration transformation system is as shown in Fig.2 and drawing of structure is as shown inFig.3. Recognition of components of vibration measuring system becomes an important partof research work. Vibration measuring system was a method developed to observe modes ofvibration of a vibrating structure. 136
  • 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME Fig.1: Mechanical Vibrator Fig.2: Mechanism Fig.4: Setup of Mechanical Structure under Vibration Fig.3: StructureELECTRONIC 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 systemand the user. The most basic microcontroller was used to perform simple math operations, controldigital outputs, and monitor digital inputs. Potentiometers were used to observe the lineardisplacement 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 observethe usefulness of the vibration measuring system designed and developed in order to measurefrequency of vibration. Experimental work covers FEM analysis, fabrication of structure, fabricationof vibration transformation mechanism, mechanical vibrator and vibration measuring system.FEM ANALYSIS With the extensive use of FEM package (ABACUS) the mechanical viability of the vibratingsystem was checked by applying different constraints and material condition. Fig.5 describes thedeflection of structure at mode-I of vibration.MATERIAL SELECTION Using software package it was easy to understand the behaviour of vibrating structure. Inorder to simplify the construction of complete system the materials were selected accordingly. Forstructure boxes aluminium was selected. Springs were used to make the joints flexible and thematerial of spring taken was spring steel. The nuts and bolts used to support the flexible joints andwere made of mild steel. The parts of vibration transformation system and vibrator system werefabricated using mild steel plates. 137
  • 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEMEFABRICATION WORK Boxes were developed with the extensive use of sheet metal work. Three boxes were made and thenassembled together. Vibration transformation mechanism system and mechanical vibrator system was fabricatedin workshop. The arrangement of cam & follower system was attached to DC motor with regulator in order tocontrol the rpm of motor and in turn vibration. The mechanical vibrator system is as shown in the Fig.6A vibration transmitting mechanism is then attached with the mechanical vibrator to achieve the vibration on thetop plate on which the structure was fixed. Aluminium structure was then fixed over the plate so that the effectof 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 asshown in the Fig.7. The readings were observed on the display attached to the system and was governed by fourdisplacement sensors. All the four displacement sensors were fixed, two on the right side and two on the leftside in between the flexible joints of two boxes. Experimental work was done to observe the frequency ofvibration at Mode-I and Mode-II of vibration for the system and was tabulated. Readings were taken for thethree 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 138
  • 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEMERESULTS AND DISCUSSIONS From the tabulated data obtained from the experimental work it was observed that thevalue of frequency was different as the vibration transformation mechanism changes. Thefrequency of vibration at mode-I of vibration was 1.7 Hz and the frequency of vibration atmode-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 plateand the supported plate in order to change the damping capacity of the structure. The secondvibration mechanism used for experimental work and the frequency of vibration at mode-I ofvibration was 5.3 Hz and the frequency of vibration at mode-II was 9.1 Hz. The mechanismwas further modified by providing bolt and a spring support to make a flexible joint at oneend between the fixed plate and the supported plate in order to set a different dampingcapacity of the structure. The third vibration mechanism was used for experimental work andthe frequency of vibration at mode-I of vibration observed was 7.12 Hz and at mode-II it was13.28 Hz. The value of frequency observed for each vibration transformation mechanism atmode-I and at mode-II of vibration was plotted as shown in Fig.8 Fig.8: Variation in the frequency with the change in mechanismCONCLUSIONS It was found that the vibration transformation mechanism plays a vital role inachieving modes of vibration. While performing experimental work the only change made inthe experimental setup was the vibration transformation mechanism, as a result of which thefrequency for the modes of vibration changes. It was observed that as the damping capacityof vibration transformation mechanism increases the frequency for the modes of vibrationincreases as shown in the Fig.8. No remarkable change was observed in the maximumdeflection of the structure at mode-I of vibration. Therefore it can be concluded that as thedamping capacity of vibration transformation mechanism increases the structures are safe andmode-I and mode-II of vibration attained will be observed at higher frequency of vibration.REFERENCES1. Yao J T P, Concept of Structural Control, Journal of Structural Division, ASCE, Vol. 98, No. 7, pp 1567-1574, 1972.2. Rayleigh, Lord, Theory of Sound (two volumes), Dover Publications, New York, reissued 1945, second edition, 1877. 139
  • 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME3. Scanlan R H, Linear damping models and causality in vibrations, Journal of Sound and Vibration, 13 (4), pp 499–503, 1970.4. Bandstra J P, Comparison of equivalent viscous damping in discrete and continuous vibrating system, Transaction of ASME, Journal of Vibration, Acoustics, Stress and Reliability in Design, 105, pp 382–392, 1983.5. Banks H T and Inman D J, On damping mechanisms in beams, Transaction of ASME, Journal of Applied Mechanics, 58, pp 716–723, 1991.6. Cremer L and Heckl M, Structure-Brone Sound, Springer-Verlag Berlin, Germany, second edition, translated by Ungar E E, 1973.7. Earls S W E, Theoretical estimation of frictional energy dissipation in a simple lap joint, Journal of Mechanical Engineering Science, 8 (2), pp 207–214, 1966.8. Beards C F and Williams J L, The damping of structural vibration by rotational slip in structural joint, Journal of Sound and Vibration, 53 (3), pp. 333–340, 1977.9. Housner G W and Masri Eds S F, Proceedings of the US National Workshop on Structural Control Research, USC Publications No. M9013, University of Southern California, 1990.10. Housner G W and Masri Eds S F, Proceedings of the International Workshop on Structural Control, University of Southern California, 1993.11. Warburton G B and Soni S R, Errors in response calculations for non-classically damped structures, Earthquake Engineering and Structural Dynamics, 5, pp 365–376, 1977.12. Hasselsman T K, Modal coupling in lightly damped structures, AIAA Journal, 14, pp 1627–1628, 1976.13. Parvin A Ma Z, The use of Helical Spring and Fluid damper Isolation Systems for Bridge Structures Subjected to Vertical Ground Acceleration, Electronic Journal of Structural Engineering, Vol. 2, pp 98-110, 2001.14. Sung Joon Kim and In Hee Hwang, Prediction of fatigue damage for composite laminate using impact response, International Journal of Fatigue, Vol 28, pp 1334–1339, 2006.15. Cawley P, Adams R D, The mechanics of the coin-tap method of non-destructive testing, Journal of Sound and Vibration, Vol. 122, pp 299–316, 1988.16. Adams R D, Cawley P, In: Sharp R S editor, Research techniques in non-destructive testing, Vibration techniques in non-destructive testing, pp 303–360, 1985.17. Damir A N, Elkhatib A and Nassef G, Prediction of Fatigue Life using Modal Analysis for Grey and Ductile Cast Iron, International Journal of Fatigue, Vol 29, pp 499–507, 2007.18. Macnaughtan M P, The cast iron brake disc developments for the 21st century, MIRA new technology 2002, Available from: http://www.atalink.co.uk/mira.htm.19. Quasar International, Inc. Using Quasar resonant inspection in a production environment; 2000, Available from: http://www.quasarintl.com/.20. Singer J, Prucz J, Influence of initial geometrical imperfections on vibrations of axially compressed stiffened cylindrical shells, J. Sound Vibration 80 (1) pp 117–143, 1982.21. Singer J, Rosen A, Influence of asymmetric imperfections on the vibration of axially compressed cylindrical shells, Israel J Technol 14, pp 23–26, 1976.22. Liu D K, Nonlinear vibrations of imperfect thin-walled cylindrical shells, Ph.D. Thesis, Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands, 1988. 140
  • 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME23. Watawala, W A Nash, Influence of initial geometric imperfections on vibrations of thin circular cylindrical shells, Grant CEE 76-14833, Department of Civil Engineering, University of Massachusetts, Amherst, 1982.24. Van Den Abeele K E, Sutin A, Carmeliet J, Johnson P, Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS), NDT & E Int. 34, pp 239–248, 2001.25. Nazarov V, Sutin A, Harmonic generation in the propagation of elastic waves in nonlinear solid media, Sov Phys Acoust 35, pp 410–413, 1989.26. Moussatov A, Castagnède B, Gusev V, Frequency up-conversion and frequency down- conversion of acoustic waves in damaged materials, Phys. Lett. A 301 pp 281–290, 2002.27. Van Den Abeele K E, Johnson P, Sutin A, Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage I. Nonlinear wave modulation spectroscopy (NWMS), Res. Nondestructr. Eval. 12, pp 17–30, 2000.28. Vila M, Vander Meulen F, Dos Santos S, Haumesser L, Bou Matar O, Contact phase modulation method for acoustic nonlinear parameter measurement in solid, Ultrasonics 42, pp 1061–1065, 2000.29. Van Den Abeele K E, Van de Velde K, Carmeliet J, Inferring the degradation of pultruded composites from dynamic nonlinear resonance measurements, Polym. Compos. 22, pp 555–567, 2001.30. Ben Tahar M, Griffa M, Elaqra H, Guerjouma R E1, Scalerandi M, Hysteretic elasticity in damaged concrete: quantitative analysis of slow and fast dynamics, Phys. Rev. B 73 (2006) 014116.31. Harik V M, Fink B K, Bogetti T A, Klinger J R, Gillespie Jr J W, 2000, Low Cycle Fatigue of Composite Structures in Army Applications: A Review of Literature and Recommendations for Research, ARL-TR-2242, Technical Report on the ARL LCF Program, U.S. Army Research Laboratory, Aberdeen, MD.32. Almroth B O, Brogan F A, Stanley G M, 1981, Structural Analysis of General Shells, Vol. II: User Instructions for the STAGS Computer Code. NASA CR-165671.33. Harik V M, Cairncross R A, Evolution of interfacial voids around a cylindrical inclusion, Journal of Applied Mechanics 66, 310–314, 1999.34. Mane S.S, Prof. Wankhede P.A, “The Design Of Vertical Pressure Vessels Subjected To Applied Forces And Vibrational Conditions” International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 2, 2012, pp. 38 - 45, Published by IAEME.35. David Asael Gutiérrez Hernández , Carlos Pérez López, Fernando Mendoza Santoyo , Juan Arturo Aranda Ruiz, “Spatial And Temporal Study Of A Mechanical And Harmonic Vibration By High Speed Optical Interferometry” International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 3 2012, pp. 96 - 106, Published by IAEME.36. Irshad M. Momin and Dr. Ranjit G. Todkar, “Design And Development Of A Pendulum Type Dynamic Vibration Absorber For A Sdof Vibrating System Subjected To Base Excitation” International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 3 2012, pp. 214 - 228, Published by IAEME 141