Effect of hyper elastic property on dynamic behaviour of IC Engine
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This paper explores the impact of hyperelastic properties of rubber pads on the dynamic behavior of internal combustion (IC) engines, using finite element analysis (FEA) to compare configurations with and without these pads. The results showed a significant reduction in vibration when rubber pads were included, validating their effectiveness as vibration absorbers. The study concludes that hyperelastic materials can greatly enhance vibration control in practical applications.
![IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 10, 2015 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 180
Effect of Hyper Elastic Property on Dynamic Behaviour of IC Engine
Nigam V Oza1
R.D.Patel2
1,2
Lecturer
1,2
Department of Mechanical Engineering
1
K.D.Polytechnic, Patan, Gujarat 2
Government Polytechnic, Vadnagar, Gujarat
Abstract— In this paper, concept of vibration absorber is
discussed with its hyperelastic properties. Rubber pads are
inserted between IC Engine and foundation. IC Engine with
and without rubber pads are dynamically analysed using
FEA software. Both modal and harmonic analysis are
performed. The FRFs of two systems are compared for their
vibration reduction. Natural frequencies and mode shapes
are obtained by modal analysis whereas FRF is obtained by
harmonic analysis in FEA software.
Key words: Hyper Elastic Property, IC Engine
I. INTRODUCTION
Vibration control and acoustics problem involves
understanding its nature such as its originating source,
vibration nature & direction and acoustics at location,
transmission path & frequency content. It is followed by
passive or active control methods. A passive control method
modifies stiffness, mass & damping of the system. Damping
can be increased by including highly damped polymeric
material at specific location onto the structure. Structure and
polymer can interact such that polymer can dissipate as
much energy as possible [1].
Rubber is one of the most important materials
included in pads and vehicle tyres. It can influence the
dynamic behaviour of pad and vehicle tyres from its
mechanical, elastic and hysteretic properties point of view.
Rubber undergoes large strains so it becomes necessary to
define rubber as a hyperelastic material [2].
When performing finite element method on rubber
type material, their elastic properties are one of input
parameters. These elastic properties are obtained by
experiments on sample of rubber in form of stress-strain
curve.
In this paper, elastic properties of rubber are
obtained from FEA software as experiment results on
sample of rubber is difficult for researchers to obtain from
companies. Rubber pads are means of dissipating energy
and acts as vibration absorber. IC Engine is founded with
and without rubber pads.
II. THEORETICAL BACKGROUND
Materials is classified based on their deformation
proportionality to load applied 1) Linear 2) Non Linear
A. Linear Elastic Behavior (Hooke’s Law)
“As the extension, so the force” as suggested by Hooke,
there exits linear relationship between force (stress) and
deflection (strain). For a spring made of steel under small
strain, the force is the product of the stiffness and the
deflection or, the deflection can be obtained by dividing the
force by the spring stiffness. As the spring remains linear
elastic, this relation is valid up to the yield point. Applying
twice the load, we obtain twice the deflection. For a linear
spring, the typical force-displacement (or stress-strain) plot
is thus a straight line, and the stiffness represents the slope
[3].
B. Hyperelastic (Neo-Hookean Law)
A hyperelastic material is still an elastic material as it
returns to its original shape after the forces have been
removed. It is also is Cauchy-elastic, which means that the
stress is determined by the current state of deformation, and
not the path or history of deformation The difference to
linear elastic Material is, that in hyperelastic material the
stress-strain relationship derives from a strain energy
density function, and not a constant factor. This definition
says nothing about the Poisson's ratio or the amount of
deformation that a material will undergo under loading
However; often elastomers are modelled as hyperelastic.
Hyperelasticity may also be used to describe biological
materials, like tissue [4].
It is very instructive to view the stress-strain
behaviour for rubber. If a tensile test is preformed on a
synthetic rubber called EPDM (Ethylene Propylene Diene
Monomer) cycled to 10%, 20%, 50% and 100% strain with
each cycle repeated twice. The stress-strain behaviour of
rubber is very different from Hooke‟s Law in four basic
areas. First, as the rubber is deformed into a larger strain
territory for the first time, it is very stiff, but upon recycling
in this same strain territory, the rubber softens dramatically.
This phenomenon is often referred to as the Mullins‟ effect.
In most applications this one time very stiff event is usually
discarded where it is assumed in these applications
repetitive behaviour will dominate. Nonlinear elasticity has
several stress and strain measures, however, it is most
common to measure elastomeric experimental data using
engineering stress and engineering strain measures, whereby
the engineering stress is the current force is divided by the
original area, and the engineering strain is the change in
length divided by the original length. All test data will use
engineering stress and engineering strain measures [3].
Fig. 1: Strain Vs Stress for Rubber like materials
III. MATERIAL MODELS FOR HYPER ELASTIC MATERIAL
As the material is incompressible, the deviatoric (subscript d
or with „bar‟) and volumetric (subscript V) terms of the
strain energy function are separated. Hence, the volumetric
term is a function of the volume ratio J only [4,5]](https://image.slidesharecdn.com/ijsrdv3i100115-160106122237/85/Effect-of-hyper-elastic-property-on-dynamic-behaviour-of-IC-Engine-1-320.jpg)
![Effect of Hyper Elastic Property on Dynamic Behaviour of IC Engine
(IJSRD/Vol. 3/Issue 10/2015/041)
All rights reserved by www.ijsrd.com 182
Fig. 8: FRF Vs Frequency plot ( IC engine with Rubber Pad)
Fig. 9: Comparison of FRF Vs Frequency plot of both case
VI. CONCLUSION
The use of hyperelastic material like rubber can greatly
reduce vibration in real application. By using FEA software,
the effect of hyperelastic behaviour of material can be
studied on dynamic behaviour of structures and FRF of the
structures can be obtained with geometry of hyperelastic
material verified for reduction of the vibration. Tuning
various dimensions and thus obtained vibration behaviour,
hyperelastic material can be incorporated as vibration
absorber in structures of real applications. FEA results also
further be used for comparison and validation with those
obtained from experiment.
REFERENCES
[1] C. Cai, H. Zheng, M. S. Khan and K. C. Hung ,”
Modelling of Material Damping Properties in ANSYS”
Defence Systems Division, Institute of High
Performance Computing
[2] Gabriel Anghelache, Raluca Moisescu, “Analysis of
Rubber Elastic Behaviour and Its Influence on Modal
Properties” MATERIALE PLASTICE, 45, Nr. 2, 2008
[3] Whitepaper MSC.Software, “Nonlinear Finite Element
Analysis of Elastomers”
[4] Roland Jakel, “Analysis of Hyperelastic Materials with
MECHANICA “ 2nd SAXSIM, 2010
[5] H. Khajehsaeid, R. Naghdabadi & J. Arghavani “A
strain energy function for rubber-like materials”
Constitutive Models for Rubber VIII – Gil-Negrete &
Alonso (eds), 2013](https://image.slidesharecdn.com/ijsrdv3i100115-160106122237/85/Effect-of-hyper-elastic-property-on-dynamic-behaviour-of-IC-Engine-3-320.jpg)
Effect of hyper elastic property on dynamic behaviour of IC Engine
- 1. IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 10, 2015 | ISSN (online): 2321-0613 All rights reserved by www.ijsrd.com 180 Effect of Hyper Elastic Property on Dynamic Behaviour of IC Engine Nigam V Oza1 R.D.Patel2 1,2 Lecturer 1,2 Department of Mechanical Engineering 1 K.D.Polytechnic, Patan, Gujarat 2 Government Polytechnic, Vadnagar, Gujarat Abstract— In this paper, concept of vibration absorber is discussed with its hyperelastic properties. Rubber pads are inserted between IC Engine and foundation. IC Engine with and without rubber pads are dynamically analysed using FEA software. Both modal and harmonic analysis are performed. The FRFs of two systems are compared for their vibration reduction. Natural frequencies and mode shapes are obtained by modal analysis whereas FRF is obtained by harmonic analysis in FEA software. Key words: Hyper Elastic Property, IC Engine I. INTRODUCTION Vibration control and acoustics problem involves understanding its nature such as its originating source, vibration nature & direction and acoustics at location, transmission path & frequency content. It is followed by passive or active control methods. A passive control method modifies stiffness, mass & damping of the system. Damping can be increased by including highly damped polymeric material at specific location onto the structure. Structure and polymer can interact such that polymer can dissipate as much energy as possible [1]. Rubber is one of the most important materials included in pads and vehicle tyres. It can influence the dynamic behaviour of pad and vehicle tyres from its mechanical, elastic and hysteretic properties point of view. Rubber undergoes large strains so it becomes necessary to define rubber as a hyperelastic material [2]. When performing finite element method on rubber type material, their elastic properties are one of input parameters. These elastic properties are obtained by experiments on sample of rubber in form of stress-strain curve. In this paper, elastic properties of rubber are obtained from FEA software as experiment results on sample of rubber is difficult for researchers to obtain from companies. Rubber pads are means of dissipating energy and acts as vibration absorber. IC Engine is founded with and without rubber pads. II. THEORETICAL BACKGROUND Materials is classified based on their deformation proportionality to load applied 1) Linear 2) Non Linear A. Linear Elastic Behavior (Hooke’s Law) “As the extension, so the force” as suggested by Hooke, there exits linear relationship between force (stress) and deflection (strain). For a spring made of steel under small strain, the force is the product of the stiffness and the deflection or, the deflection can be obtained by dividing the force by the spring stiffness. As the spring remains linear elastic, this relation is valid up to the yield point. Applying twice the load, we obtain twice the deflection. For a linear spring, the typical force-displacement (or stress-strain) plot is thus a straight line, and the stiffness represents the slope [3]. B. Hyperelastic (Neo-Hookean Law) A hyperelastic material is still an elastic material as it returns to its original shape after the forces have been removed. It is also is Cauchy-elastic, which means that the stress is determined by the current state of deformation, and not the path or history of deformation The difference to linear elastic Material is, that in hyperelastic material the stress-strain relationship derives from a strain energy density function, and not a constant factor. This definition says nothing about the Poisson's ratio or the amount of deformation that a material will undergo under loading However; often elastomers are modelled as hyperelastic. Hyperelasticity may also be used to describe biological materials, like tissue [4]. It is very instructive to view the stress-strain behaviour for rubber. If a tensile test is preformed on a synthetic rubber called EPDM (Ethylene Propylene Diene Monomer) cycled to 10%, 20%, 50% and 100% strain with each cycle repeated twice. The stress-strain behaviour of rubber is very different from Hooke‟s Law in four basic areas. First, as the rubber is deformed into a larger strain territory for the first time, it is very stiff, but upon recycling in this same strain territory, the rubber softens dramatically. This phenomenon is often referred to as the Mullins‟ effect. In most applications this one time very stiff event is usually discarded where it is assumed in these applications repetitive behaviour will dominate. Nonlinear elasticity has several stress and strain measures, however, it is most common to measure elastomeric experimental data using engineering stress and engineering strain measures, whereby the engineering stress is the current force is divided by the original area, and the engineering strain is the change in length divided by the original length. All test data will use engineering stress and engineering strain measures [3]. Fig. 1: Strain Vs Stress for Rubber like materials III. MATERIAL MODELS FOR HYPER ELASTIC MATERIAL As the material is incompressible, the deviatoric (subscript d or with „bar‟) and volumetric (subscript V) terms of the strain energy function are separated. Hence, the volumetric term is a function of the volume ratio J only [4,5]
- 2. Effect of Hyper Elastic Property on Dynamic Behaviour of IC Engine (IJSRD/Vol. 3/Issue 10/2015/041) All rights reserved by www.ijsrd.com 181 )() 2 , 11 ( JvWIIdWW (1) )() 32 , 1 ( JvWdWW (2) So, Wd is the strain energy necessary to change the shape, WV the strain energy to change the volume. A. Polynomial Form k J N k kD N ji j I i IijCW 2 )1( 1 1 1 )32()31( (3) The Cij and Dk are material constants which have to be determined by tests. Here, the strain energy function is a polynomial function. Depending on its order, no (=single curvature), one or more inflection points in the stress-strain curve may appear. For the higher order functions, enough test data has to be supplied. Hyperelastic material laws are: 1) Neo-Hookean: 2 )1( 1 1 )3 1 (10 eJ D ICW (4) 2) Mooney-Rivlin: 2 )1( 1 1 )3 1 (01)3 1 (10 eJ D ICICW (5) B. Polynomial Form of Order 4 1)e(J 2D 12 1)e(J 1D 12 3) 1I(20C3) 1I(10CW (6) Where I1 is variant IV. FINITE ELEMENT ANALYSIS Components of IC engine are modelled with structure steel. IC engine is modelled with or without Rubber pad and meshed for finite element analysis. Modal and harmonic analysis are performed on both models. Neoprene Rubber is selected in material data. Hyper elastic property is obtained from FEA software. Neo-Hookean curve fitting method selected in FEA software environment and shear modulus and incompressibility parameter are obtained by Neo- Hookean. Fig 2: Case1: IC engine without rubber pad (a) Solid and (b) FEM model Fig 3: Case 2: IC engine with rubber (a) Solid and (b) FEM model V. RESULT AND DISCUSSION For both the cases, natural frequency is listed in Table 1 and mode shapes are plotted as shown in figure 4 to figure 6. Frequency (Hz.) Frequency Response (mm) % age variation in Frequency Response Case 1 (Without Rubber pad) Case 2 (With Rubber pad) 73 1.31e-06 2.68e-7 -79.54 186 4.13e-6 4.59e-6 11.13 235 1.73e-4 5.55e-5 -67.91 Table 1: Comparison of Frequency Response (a) case 1 (b) case 2 Fig. 4: First Mode Shape (a) case 1 (b) case 2 Fig. 5: Second Mode shape (a) case 1 (b) case 2 Fig. 6: Third Mode shape FRF for both cases are plotted in figure 7 and 8. In figure 9 and table 1, FRF and natural frequency for both cases are compared. It is evident from figure 9 that with addition of rubber pad, FRF changes. Also in percentage variation, negative sign indicates decrease in FRF while positive sign indicates increase in FRF. Fig. 7: FRF Vs Frequency plot (IC engine without Rubber Pad)
- 3. Effect of Hyper Elastic Property on Dynamic Behaviour of IC Engine (IJSRD/Vol. 3/Issue 10/2015/041) All rights reserved by www.ijsrd.com 182 Fig. 8: FRF Vs Frequency plot ( IC engine with Rubber Pad) Fig. 9: Comparison of FRF Vs Frequency plot of both case VI. CONCLUSION The use of hyperelastic material like rubber can greatly reduce vibration in real application. By using FEA software, the effect of hyperelastic behaviour of material can be studied on dynamic behaviour of structures and FRF of the structures can be obtained with geometry of hyperelastic material verified for reduction of the vibration. Tuning various dimensions and thus obtained vibration behaviour, hyperelastic material can be incorporated as vibration absorber in structures of real applications. FEA results also further be used for comparison and validation with those obtained from experiment. REFERENCES [1] C. Cai, H. Zheng, M. S. Khan and K. C. Hung ,” Modelling of Material Damping Properties in ANSYS” Defence Systems Division, Institute of High Performance Computing [2] Gabriel Anghelache, Raluca Moisescu, “Analysis of Rubber Elastic Behaviour and Its Influence on Modal Properties” MATERIALE PLASTICE, 45, Nr. 2, 2008 [3] Whitepaper MSC.Software, “Nonlinear Finite Element Analysis of Elastomers” [4] Roland Jakel, “Analysis of Hyperelastic Materials with MECHANICA “ 2nd SAXSIM, 2010 [5] H. Khajehsaeid, R. Naghdabadi & J. Arghavani “A strain energy function for rubber-like materials” Constitutive Models for Rubber VIII – Gil-Negrete & Alonso (eds), 2013