Since the innovation of cars, the measure of autos on the route around the universe is increasing over the old ages. In Malaysia, 548 115 motor vehicles were registered in the twelvemonth 2008 compared with merely 97 262 registered in the twelvemonth 1980 [ 1 ] . With autos and roads, work forces can go from one topographic point to another with easiness. Apart from that, it is of import to guarantee the journey is safe and comfy. This could be done by the auto suspension system. It is playing a major function in maintaining the auto in control while weakening the unpleasant daze due to abnormalities on the roads travelled.
Proton New Saga ( besides known as Proton BLM ) was launched in January 2008. It is an low-cost rider auto with a capacity of 5 riders. Besides, it is equipped with MacPherson prances and a stabilizer saloon in the forepart suspension system and tortuosity beam axle in the rear suspension system. The Proton New Saga is good received as evidenced by engagements of more than 120 000 units since its launch [ 2 ] .
1.2 Problem Statement
The success in Proton New Saga does non halt Proton from willing to better this auto theoretical account. Surveies on the rear suspension system are indispensable in order to farther heighten the handling and sit comfort of this popular auto [ 3 ] . Modal analysis is needed, particularly, in order to analyze its quiver behaviour. Besides finding the natural frequences and manner forms, the result of a average analysis can besides be used to execute more elaborate dynamic analyses.
The tortuosity beam axle found on the rear suspension system of Proton New Saga has an inverted “ V ” cross-sectional form. Other auto theoretical accounts with similar rear suspension system such as Perodua Myvi and Toyota Vios have a “ U ” cross-sectional form tortuosity beam axle. However, the “ unfastened ” side of the “ U ” cross-sectional form tortuosity beam axle on Perodua Myvi is oriented toward the forepart of the auto while the Toyota Vios is oriented toward the rear of the auto. Consequently, it is of involvement to analyze the consequence of the cross-sectional form of the tortuosity beam axle on the quiver behaviour.
The aims of this thesis are:
To pattern the Proton New Saga tortuosity beam axle by utilizing finite component package.
To execute average analysis on the Proton New Saga tortuosity beam axle.
To compare the quiver behaviour of different cross-sectional form tortuosity beam axles.
2.1 Vehicle Suspension System
The suspension system of a vehicle is the construction which links the wheel to the vehicle organic structure while allows comparative gesture between them [ 4 ] . It has two of import maps. The primary map is to insulate the vehicle construction whenever operable from daze burden and quiver due to abnormalities of the route surface travelled. Furthermore, the suspension system must at same clip, maintains the stableness, maneuvering and general managing qualities of the vehicle. The first demand can be met by utilizing flexible elements and dampers. On the other manus, the 2nd map can be achieved by commanding the comparative gesture between unsprung multitudes – wheel-and-axle assemblies – and the sprung mass by the usage of mechanical linkage [ 5 ] .
2.1.1 Types of Vehicle Suspension System
The vehicle suspension systems can be by and large categorised into dependent and independent types [ 6 ] . In a dependent suspension system, two wheels are physically linked by a stiff axle whereby common wheel influence exists between the wheels connected by the axle. Solid-axle, torsion-beam axle, De Dion axle are the illustrations of dependent suspension systems. On the other manus, in an independent suspension system, the perpendicular gesture of one wheel does non impact straight the gesture of another wheel. Some of the common independent suspension systems include dual wishing bone suspensions, MacPherson struts suspension, draging arm suspension, and multilink suspension.
2.1.2 Torsion beam Axle Suspension System
Torsion beam axle suspension system is besides called twist-beam suspension. It is frequently used as the rear suspension in front-engine, front wheel thrust ( FF ) type vehicles since it has less parts and simple constellation. The tortuosity beam axle suspension system consists of two draging weaponries that are welded to a twistable cross-member ( frequently torsion beam ) and fixed to organic structure through draging links with bushing. This twistable beam absorbs all perpendicular and sidelong force minutes [ 7 ] . It must be stiff plenty to back up sidelong forces during cornering and, at the same clip, be flexible plenty to let the right- and left-hand wheels to displace otherwise when driving over a bump. The comparative balance between the stiffness and the flexibleness of the component members has to be considered during the design phase in malice of the simple constellation [ 8 ] .
Analysiss have to be done on the tortuosity beam axle suspension system in order to measure its public presentation. It has to be analysed in footings of structural strength, lastingness, and kinematic and conformity characteristic. Modal analysis can be performed to analyze the quiver features of the suspension system [ 3 ] . On the other manus, the elasto-kinematic analysis can be performed by utilizing multibody method where the tortuosity beam has to be modelled as a flexible organic structure [ 9 ] .
Figure 2.1. A typical tortuosity beam axle suspension system [ 8 ] .
This suspension type has many advantages in footings of installing, suspension and kinematics.
From an installing point of position:
the assembly and dismantlement are easy ;
small infinite is needed ;
springs and daze absorbers can be easy fitted ;
few constituents to be handled.
From a suspension point of position:
there is a favorable wheel to spring damper ratio ;
springing is barely affected since there are merely two bearing points ;
low unsprung multitudes ;
the cross-member can work as an anti-roll saloon [ 7 ] .
From a kinematic point of position:
toe-in and path breadth alteration on mutual and parallel springing is negligible ;
the alteration of camber under sidelong forces is low ;
the load-dependent organic structure axial rotation understeering of the whole axle is low ;
good radius-arm axis location whereby tail-lift during braking could be reduced [ 7 ] .
However, there are besides disadvantages for this type of suspension system. The disadvantages are:
a inclination to sidelong force oversteer as a consequence of control arm distortion ;
tortuosity and shear emphasis exist in the cross-member ;
there is high emphasis in the dyer’s rocket seams, hence, the allowable rear axle burden is limited ;
the limited kinematic and elasto-kinematic chances for finding the wheel place ;
the constitution of the place of the instantaneous Centre by agencies of the axle kinematics and rigidness of the torsion-beam axle ;
there is common consequence on the wheels ;
the hard decoupling of the quiver and noise from the route surface ;
the considerable demand for stableness of the bodywork in the part of those points on the forepart bearings where complex, superposed forces have to be transmitted [ 7 ] .
Owing to the advantages of tortuosity beam axle suspension system, it is widely adopted in rider auto, particularly in the rear suspension of hatchback. Some illustrations of rider autos available in Malaysia which use tortuosity beam axle as rear suspension system are Proton New Saga, Proton Savvy, Proton Exora, Perodua Myvi, Perodua Viva, Toyota Altis, Toyota Vios, Honda City, Nissan Grand Livina, etc.
Vibration is any gesture that repeats itself after an interval of clip. By and large, a vibratory system includes a agency for hive awaying possible energy ( spring or snap ) , a agency for hive awaying kinetic energy ( mass or inactiveness ) , and a agency by which energy is bit by bit lost ( damper ) . In vibratory systems, possible energy is transferred to kinetic energy and kinetic energy to possible energy alternately. If damping exists, some energy is dissipated in each rhythm of quiver and the quiver will finally decease out [ 10 ] .
In order to analyze the quiver of a dynamic system, it is of import to cognize the figure of grades of freedom of the system before continuing to analysis. The grade of freedom of a vibratory system is defined as the minimal figure of independent co-ordinates required to find wholly the gesture of all parts of the system at any blink of an eye of clip [ 11 ] .
Vibration can be classified into free or forced quivers. Free quiver takes topographic point when a system oscillates under the action of forces built-in in the system itself, and when external impressed forced are absent. The system under free quiver will vibrate at one or more of its natural frequences. The natural frequences are belongingss of a dynamical system established by its mass and stiffness distribution [ 12 ] .
Forced quiver is the quiver that takes topographic point under excitement of external forces. A system will be forced to vibrate at the excitement frequence if the excitement is oscillating. If the frequence of excitement coincides with one of the system ‘s natural frequences, resonance occurs. When resonance occurs, perilously big oscillations may ensue and do failure to the system. Therefore, the computation of the natural frequences is of critical importance in the survey of quivers [ 12 ] .
A quiver is known as undamped quiver if no energy is lost or dissipated in clash or other opposition during oscillation. On the other manus, if any energy is lost in this manner, it is called damped quiver. In many physical systems, the sum of damping is so little that can be neglected for most technology intents. However, consideration of muffling becomes highly of import in analysing vibratory systems near resonance [ 10 ] .
Vibrations can besides be categorised as additive quiver or nonlinear quiver. If all the basic constituents of vibratory system ( the springs, mass, and damper ) behave linearly, the ensuing quiver is known as additive quiver. However, if any of the basic constituents behave nonlinearly, the quiver is called nonlinear quiver. All vibratory systems tend to act nonlinearly where the rule of superposition is non valid [ 10 ] .
2.3 Finite Element Method
The finite component method ( FEM ) , sometimes called finite component analysis ( FEA ) , is a computational technique used to obtain approximative solutions of boundary value jobs in technology. A boundary value job, besides called field job, is a mathematical job in which one or more dependent variables must fulfill a differential equation everyplace within a known sphere of independent variables and fulfill specific conditions on the boundary of the sphere. The field is the sphere of involvement and most frequently represents a physical construction. The field variables are the dependent variables of involvement governed by the differential equation. They may include physical supplanting, temperature, heat flux, fluid speed and so on. On the other manus, the boundary conditions are the specified values of the field variables ( or related variables such as derived functions ) on the boundaries of the field [ 13 ] .
2.3.1 How Does Finite Element Method Work?
Figure 2.1 shows a volume of some stuffs with known physical belongingss. The volume represents the sphere of a boundary value job to be solved. For simpleness, it is assumed to be a planar instance with a individual field variable I• ( x, y ) to be determined at every point P ( x, y ) such that a known government equation is satisfied precisely at every such point. This implies an exact mathematical solution is obtained. The solution is a closed-form algebraic look of the independent variables. However, the sphere may be geometrically complex in practical jobs. Therefore, approximative solutions based on numerical techniques and digital calculation are most frequently obtained in technology analyses of complex jobs [ 13 ] .
Figure 2.2. ( a ) A general planar sphere of field variable I• ( x, Y ) . ( B ) A three-node finite component defined in the sphere. ( degree Celsius ) Additional elements demoing a partial finite component mesh of the sphere [ 13 ] .
Figure 2.2 ( B ) shows a little triangular component that encloses a finite-sized subdomain of the country of involvement. This component is non a differential component of size dx A- Dy makes this a finite component. The vertices of the triangular component are nodes. A node is a specific point in the finite component at which the value of the field variable is to be computed, explicitly. Nodes located on the boundaries of the finite component are called exterior nodes. They may be used to link an component to adjacent finite component. Interior nodes, meanwhile, do non lie on the finite component boundaries and can non be connected to any other finite component. The figure of grades of freedom associated with a finite component is equal to the merchandise of the figure of nodes and the figure of values of the field variable ( and perchance its derived functions ) that must be computed at each node [ 13 ] .
In finite component method, the values of the field variable computed at the nodes are used to come close the values at nonnodal points by insertion of the nodal values. This is the Southern Cross of finite component method. For the three-node trigon illustration, the nodes are all exterior. At any other point within the component, the field variable is described by the approximative relation
aˆ¦aˆ¦aˆ¦aˆ¦ . ( 2.1 )
where I•1, I•2, and I•3 are the values of the field variable at the nodes while N1, N2, and N3 are the insertion maps. The insertion maps are predetermined, known maps of the independent variables. These maps describe the fluctuation of the field variable within the finite component [ 13 ] .
The finite component equations are formulated such that, at the nodal connexions, the value of the field variable at any connexion is indistinguishable for each component connected to the node. As a consequence, continuity of the field variable at the nodes and across interelement boundaries is ensured [ 13 ] .
2.3.2 General Procedure for Finite Element Analysis
There are certain common stairss in explicating a finite component analysis of a physical job, whether structural, heat transportation, fluid flow, or some other job. These stairss are normally embodied in commercial finite component package bundles. The stairss are described as follows [ 13 ] .
The preprocessing stairss is described by and large as specifying the theoretical account and includes
Specify the geometric sphere of the job.
Specify the component type to be used.
Specify the stuff belongingss of the elements.
Specify the geometric belongingss of the elements ( length, country and the similar ) .
Specify the component connectivities ( engage the theoretical account ) .
Specify the physical restraints ( boundary conditions ) .
Specify the burdens [ 13 ] .
The preprocessing ( exemplary definition ) measure is highly of import. A absolutely computed finite element solution is of perfectly useless if it corresponds to the incorrect job [ 13 ] .
In this measure, finite component package assembles the regulating algebraic equations in matrix signifier and computes the unknown values of the primary field variables. Then, the computed values are used by back permutation to execute calculation on the extra, derived variables, such as reaction forces, component emphasiss, heat flow, etc [ 13 ] .
However, it is really common for a finite component theoretical account to be represented by figure of equations. Particular solution techniques are used to cut down informations storage demands and calculation clip. For illustration, in inactive, additive jobs, a moving ridge forepart convergent thinker, based on Gauss riddance, is normally used [ 13 ] .
In postprocessing measure, the analysis and rating of the solution consequences are performed. Postprocessor package contains sophisticated modus operandis used for screening, printing, and plotting selected consequences from a finite component solution. The operations that can be accomplished by the postprocessor package include
Sort component emphasiss in order of magnitude.
Calculate factors of safety.
Plot deformed structural form.
Animate dynamic theoretical account behaviour.
Produce color-coded temperature secret plans [ 13 ] .
Although solution informations can be manipulated many ways in postprocessing, the most of import aim is to use sound technology opinion in finding whether the solution consequences are physically sensible [ 13 ] .
Engagement is the procedure of stand foring a physical sphere with finite elements. It consequences set of elements, known as the finite component mesh. It is by and large impossible to include the full physical sphere in the component mesh if the sphere includes curving boundaries. However, by utilizing smaller and more legion elements, more of the physical sphere can be included and the curving boundaries are more closely approximated. As the insertion maps satisfy certain mathematical demands, a finite component solution for a peculiar job converges to the exact solution of the job. This can be done by increasing the figure of elements while diminishing the physical dimensions of the elements [ 13 ] .
Figure 2.3. ( a ) Arbitrary curved-boundary sphere modelled utilizing square elements. Stippled countries are non included in the theoretical account. A sum of 41 elements is shown. ( B ) Refined finite component mesh demoing decrease of the country non included in the theoretical account. A sum of 192 elements is shown. [ 13 ]
The chief concern of this undertaking is to compare the quiver behaviour of different cross-sectional form tortuosity beam axles. Modal analysis has to be performed to find the natural frequences and mode forms of the tortuosity beam axles. Due to the big size of the specimen ( tortuosity beam axle ) and deficiency of appropriate equipments, experimental method can non be used. However, with the available of finite component package bundle, such as Abaqus Unified FEA and ANSYS Multiphysics, finite component analysis can be used to obtain approximative consequences.
3.2 Materials and Equipments
In this undertaking, the Abaqus Unified FEA package was used due to its strong ability to work out nonlinear jobs. The tortuosity beam axle is suited to be modelled by utilizing Abaqus Unified FEA since it behaves nonlinearly. Besides, the package can be used as preprocessor, convergent thinker and besides the postprocessor. Surely, average analysis can besides be performed by utilizing it.
Besides, high public presentation computing machine was used to execute the finite component analysis as the analysis is a heavy undertaking. The higher public presentation computing machine used will ensue faster analysis.
First, the dimension of the tortuosity beam axle of a Proton New Saga was requested from Proton. The geometry was so modelled. Mesh coevals was performed after geometry modeling. After that, modal analysis was performed to find the natural frequences and the corresponding manner forms. Merely the first 10 natural frequences and manner forms will be taken. The geometry modeling, engaging and average analysis were performed by utilizing Abaqus Unified FEA. The same processs were repeated for “ U ‘ cross-sectional form tortuosity beam axle. Consequences for the two different cross-sectional form tortuosity beam axles were so compared.