HORIZONTAL DISPLACEMENT OF LAMINATED RUBBER-METAL SPRING FOR ENGINE ISOLATOR

Transcription

1 VOL., O. 7, SEPTEMBER ISS 89-8 ARP Journal of Engineering and Applied Sienes - Asian Researh Publishing etwor (ARP). All rights reserved. HORIZOTAL DISPLACEMET OF LAMIATED RUBBER-METAL SPRIG FOR EGIE ISOLATOR M. A. Salim, A. Putra and M. A. Abdullah 3 Green Tehnolog Vehiles, Fault of Mehanial Engineering, Universiti Tenial Malasia Melaa, Malasia Sustainable Maintenane Engineering, Fault of Mehanial Engineering, Universiti Tenial Malasia, Malasia 3 Advaned Vehile Tehnolog, Fault of Mehanial Engineering, Universiti Tenial Malasia, Malasia azli@utem.edu.m ABSTRACT This paper presents the stud on horizontal displaement of laminated rubber-metal spring on engine isolator. Initiall, lumped model is adopted in the analtial sstem of isolator for one degree of freedom sstem. Later, the power series tehnique is used to develop more omplex analsis. In this model, natural rubber is used for isolator rod and the metal plate is reinfored inside the rod. This plate used to divide the natural rubber rod into more degree of freedom. Two tpes of results are reorded whih are surfae and standalone displaements. In these two displaements, the results show the displaement in axial axis is inreased b inreasing the number of metal plate. It happens beause natural rubber properties have been influened b metal plate and finall unique ompressibilit behavior ourred. Kewords: LR-MS, displaement, natural rubber, metal plate and spring. ITRODUCTIO In pratie, natural rubber (R) is a versatile and exellent material beause in ears it was suessfull used in man engineering appliations []. The appliations an be found in ivil, railwas, offshore, automotive, defene, aerospae and man more industries. It beomes number one hosen material due to the abilit to withstand large deformations and store more elasti energ per unit volume ompare other materials []. It also has inherent damping and spring-lie performane in term of vibration resonant. Besides, R also has their unique response whih is ver little ompressibilit during the appliation of exitation fore. Rubber bearings were developed for stress distribution and stress onentration of a laminated elastomeri bearing subjeted to axial loads []. In this stud, finite element (FE) approah is used to produe approximated solution. Aording to this stud, the benefit of using R is based on shape fator. It is beause of the edge effet of the material is dereased when the shape fator is inreased. The shape fator is one of the important parameters whih an influene the flexibilit of the material in order to blo the unwanted energ transmitted into the sstem. In 7, this researh was omplied with other researhers who studied the use of rubber bearings for new highwa onstrution in Greee [3]. The rubber bearings are used as a supports for the highwa bridges. In this stud, two samples were used and loated at the bridge olumn. Test result shows the stiffness and damping ratio have a good relationship with axial load as well as the frequen of the horizontal displaement. The total displaement of rubber bearings is proportional to the fore appl. In, the stud of laminated rubber bearing for earthquae phenomenon is found. This researh is started b modelling of the hstereti behaviour of rubber bearings under uni-diretional horizontal displaement and onstant horizontal ompressive load [4]. Three tpes of bearing are used in these studies whih are R bearing, lead rubber bearing and high damping rubber bearing. Man experiments were onduted to analsis the bearings suh as basi test, multi-step relaxation, li test and simple relaxation. Finall, the researhers found that the R bearing gives a better result ompared to others in term of rate-dependent rheolog. Man researhes of laminated rubber bearings were onduted and foused on horizontal displaement of the bearings. All of the researhes in previous disussion are onentrated in ivil engineering fields. However, there are some researhes where the laminated rubber bearings are adopted and applied in automotive industries. In automotive industries, internal ombustion engine (ICE) is a one essential parts inside the ar. oise and vibration generated b the engine annot be negleted and it is annoing. These are beause of the natural behaviour and fundamental soure from engine motion [,]. Man efforts were performed to investigate this phenomenon whih is tring to redue the vibrations and finall the driver and passengers are in omfort. The researhers suggested that, b designing new engine mounting using R, the unwanted noise and vibration are potentiall ut off. However, this design onl apable to use in ertain range of frequen and not suitable for automotive engine. In this paper, the horizontal displaement of laminated rubber-metal spring (LR-MS) is studied. The basi model is developed using lumped parameter and omplex model is elaborated using power series tehnique. Initiall, the R is used as a basi isolator for automotive engine and metal plate is inserted one b one depends on how man degree of freedom (DOF) is needed. B inserting the metal plate, the lumped model beomes more omplex and power series will help to minimize the omplexit of the modelling in multi-bod relationship. The horizontal displaement is important parameters beause the results will show the ompressibilit amount 784

2 VOL., O. 7, SEPTEMBER ISS 89-8 ARP Journal of Engineering and Applied Sienes - Asian Researh Publishing etwor (ARP). All rights reserved. that an be bloed b the LR-MS during exitation fore appliation. RESEARCH METHODOLOGY This setion desribes the mathematial model development of laminated rubber-metal plate (LR-MS) using lumped parameter method. This stud was onduted at Fault of Mehanial Engineering (FKM), Universiti Tenial Malasia Melaa (UTeM). In this method, the phsial sstem is initiall started with massdamper-spring model. Aording to method, the depth of understanding on phsial model of the sstem is neessar before the derivation. In lumped sstem there are two parts needed to be onsidered whih the first one is mass and the seond are damper and stiffness. The shemati diagram for basi lumped model is shown in Figure-. Figure-. Two DOF of the sstem for LR-MS. The flexible struture is designed to mae the surfae vibrates easil and representing the free boundar ondition for LR-MS. The fixed struture representing the fixed boundar ondition and there is no displaement happen. There are two tpes of fore involved whih are exitation fore, and transmitted fore. The exitation fore is the vibration fore from vibrating soure and then transmitted to the LR-MS. Finall the transmitted vibration energ was ourred at fixed struture and alled transmitted fore. The EOM and matrix form for two DOF are shown in Eqns. (3) and (4) m (3) Figure-. Shemati diagram of basi lumped model. m (4) m The equation of motion (EOM) for this lumped sstem an be derived into mathematial expression and shown in Eqn. (). m () In a matrix form, the EOM beomes m () In this stud, part one is represented the metal plate and part two is represented the natural rubber (R), respetivel. For metal plate, the important parameter is onl the total of mass and for R are stiffness and damping oeffiient. The objetive using the metal plate is to divide the R rod will inrease the degree of freedom (DOF) of the sstem itself. Aording to this statement, one DOF is not signifiant for adding the metal plate beause the R rod is alread in one DOF. B adding metal plate, the LR-MS is reated. The two DOF of the sstem is showed in Figure- where mass of metal plate and is rigid mass. General lumped parameter method is shown in Figure-3. B using power series tehnique, the general equation of the sstem is developed. The formulation is started from the delaration of the highest DOF of the sstem. Let sa the highest DOF of the sstem in and this number will be represented the final DOF. The number of an be from to infinite number. Let tae is the highest DOF where this number onsidered the highest value of mass m and in mathematial expression in an be written as m. Using the power series, the new mathematial expression an be represented as m(+)-. The arra for the power series an written as m m () m m () m m (7) 3 4 m m (8) 4 3 m m (9) m m () 784

3 VOL., O. 7, SEPTEMBER ISS 89-8 ARP Journal of Engineering and Applied Sienes - Asian Researh Publishing etwor (ARP). All rights reserved In shemati diagram of lumped parameter method in power series tehnique for LR-MS is shown in Figure-3. Figure-3. Lumped parameter in power series tehnique for LR-MS. The mathematial expression for LR-MS using power series tehnique is shown in Eqn. () m m m () R material is used beause of the flexibilit propert whih offers a major advantage to the sstem. This propert an at as a spring to blo the vibration energ in ertain amount before pass through the material. It is able to sustain large displaement. However, R has disadvantages when the material is subjeted to large stati preload. This material is inompressible affeted in solid blo ondition where a preload will ause the material to bulge outward [7-]. In this phenomenon, bulge not onl dereases the dnami performane of the material but it is also redues a life time of the material itself. The bulge effet an be solved b two methods. The first method is large dnami preload is applied to replae the large stati preload. The seond method is the effet an be ountered b inreasing the stiffness of the LR-MS. In this wa, implementation of metal plate b insertion in R rod is one of the alternatives and the shemati diagram is shown in Figure-4. B inreasing the stiffness in horizontal axis, it is believed that the bulging effet an be prevented and maes the rod more stable. Figure-4. Bulging effet at R rod. RESULTS AD DISCUSSIO In this stud, it was pointed out that the displaements of the LR-MS sstem are in multi DOF when the exitation fore is applied at the top of the sstem in horizontal axis. The horizontal displaement results are reorded from one to six DOF. There are two tpes of displaement whih are surfae and standalone. Surfae displaement happen onl at the top of the LR-MS sstem but for standalone, the displaement reorded at eah of the embedded metal plate and R. The number of data is based on the number of DOF. Surfae and overall displaement are shown in Figure-, Figure- and Figure- 7. Aording to the results, the frequen range is from to Hz. There are man definitions regarding the low and high frequen. In this stud, range to Hz is delared as a low frequen. This statement is supported b maximum amplitude ourred at low frequen. Low frequen is important issue and it needs to be disussed further beause man vibration phenomena in industr happen in low frequen region. In Figure-, the maximum displaement is reorded as.9 x -3 mm at 4 Hz for six DOF and minimum displaement of 4.8 x -4 mm at 4. Hz for one DOF. These two results are supported previous statement whih displaement or amplitude is inversel proportional to frequen range. At one DOF, the result shows low displaement beause there is no metal plate embedded inside the R. Theoretiall, R has ver little ompressibilit if there are no an other materials influene their properties []. For six DOF results, maximum displaement is shown ompared to others. Generall, metal plate an at as reinforement at the

4 VOL., O. 7, SEPTEMBER ISS 89-8 ARP Journal of Engineering and Applied Sienes - Asian Researh Publishing etwor (ARP). All rights reserved. middle of R and finall influenes the R properties and signifiant ompressibilit happen inside the LR-MS. In term of displaement, b dereasing the DOF of R, small displaement is reorded. Other than that, the graph has a pea and it bends where the urve is depended on the oeffiient of the linear term whih depends on the amplitude of the exitation fore. The bend is proportional relation to the fore applied. Figure-7 shows the various results for standalone displaement from one to six DOF. The number of standalone displaement is depending on the number of DOF of LR-MS. Aording to these results, the standalone displaement is dereased b the inrement of the number of metal plate. The number of metal plate influenes the number of DOF and finall axial ompression inreased due to the ompressibilit behaviour of R material. In ontrast, b adding the metal plate in R, the standalone displaement is slowl dereasing in axial diretion. COCLUSIOS LR-MS model is developed for automotive engine isolator. The lumped model and the power series tehnique are used to develop multi DOF of LR-MS. This sstem has been solved and bloed the vibration energ at high frequenies. However, the maximum displaement is reorded when number of the metal plate and DOF are inreased simultaneousl. This happen beause of R properties where it is influened b metal plate and finall abnormal ompressibilit behaviour ourred. Figure-. Comparison for surfae displaement of LR- MS. Figure-. Surfae displaement for LR-MS. 7844

5 VOL., O. 7, SEPTEMBER ISS 89-8 ARP Journal of Engineering and Applied Sienes - Asian Researh Publishing etwor (ARP). All rights reserved. Figure 7. Standalone displaement on LR-MS for MDOF. ACKOWLEDGEMETS The authors would lie to than the Fault of Mehanial Engineering (FKM), Universiti Tenial Malasia Melaa (UTeM) for finanial support under PJP/3/FKM/PROTOTAIP/S87 and PJP/3/FKM (B)/S4. REFERECES [] R Tehnial Bulletin. 99. Engineering design with natural rubber. The Malasian Rubber Produers Researh Assoiation. [] M. Imbimbo and A. De Lua F.E. stress analsis of rubber bearings under axial loads. Computers and Strutures. Vol. 8, pp [3] G. C. Manos, S. Mitoulis, V. Kourtidis, A. Sextos and I. Tegos. 7. Stud of the behavior of steel laminated rubber bearings under presribed loads. In: th World Conferene on Seismi Isolation, Energ Dissipation and Ative Vibrations Control Strutures. [4] A. R. Bhuian, Y. Oui, M. K. Razza and A. F. M. S. Amin.. Earthquae resistant design of highwa bridges using laminated rubber bearings: An approah for modeling hstereti behavior based on experimental harateristi of rheolog properties. In: 3rd International Earthquae Smposium. pp [] G. Y. Pan, X. Yang and Y. Yan. 4. Optimization of vehile powertrain mounting sstem and its performane. Applied Mehanis and Materials. pp [] Z. Xie, D. Yu and R. Li. 3. Multi-objetive robust optimization design of vehile engine mount sstems. QiheGongheng / Automotive Engineering. Vol. 38, o., pp [7] J. R. Banerjee. 4. Development of an exat dnami stiffness matrix for free vibration analsis of a twisted Timosheno beam. Journal of Sound and Vibration. Vol. 7, pp

6 VOL., O. 7, SEPTEMBER ISS 89-8 ARP Journal of Engineering and Applied Sienes - Asian Researh Publishing etwor (ARP). All rights reserved. [8] R. A. Ibrahim. 8. Reent advanes in nonlinear passive vibration isolators. Journal of Sound and Vibration. Vol. 34, pp [9] M. A. Salim, A. Putra and M. A. Abdullah. 4. Analsis of axial vibration in the laminated rubbermetal spring. Advaned Materials Researh. Vol. 84, pp. 4-. [] M. A. Salim, A. Putra. D.J. Thompson,. Ahmad and M. A. Abdullah. 3. Transmissibilit of a laminated rubber-metal spring: A preliminar stud. Vol. 393, pp. -. [] M. K. James and M. T. Shahzod. 7. Tension Buling in multilaer elastomeri isolation bearings. Journal of Mehanis of Materials and Strutures. Vol., o. 8, pp