International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
#1
*2
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PG Student,*Assistant Professor&Mechanical Engineering Department&NMU,Jalgaon.
SSBT’s College of Engineering & Technology, Jalgaon, Maharashtra, India.
Abstract - The aim of this paper is to review general study on the design, analysis and optimization of composite leaf spring with an emphasis on TLBO technique. Leaf springs are commonly used in the suspension system of automobiles and are subjected to millions of varying stress cycles leading to fatigue failure. The suspension system in an automobile significantly affects the behavior of vehicle, i.e. vibrational characteristics including ride comfort, directional stability, etc. If the unsprung weight is reduced then fatigue stress induced in the leaf spring is also reduced. Leaf spring contributes for about 10-
20% of unsprung weight. Hence even a small amount of weight reduction in leaf spring will lead to a passenger comfort as well as reduction in vehicle cost.
The replacement of steel by composite material along with an optimum design will be a good contribution in the process of weight reduction of leaf spring. Various methods are used in design optimization of leaf spring, most of which use mathematical programming techniques. In this paper, we are presenting Teaching
Learning Based Optimization (TLBO) as a formulation and solution technique. By applying
TLBO, the optimum dimensions of leaf spring will be obtained, which contribute towards achieving the minimum weight with adequate strength and stiffness.
Keywords —Leaf Spring, Composite Material,
Teaching Learning Based Optimization, Design optimization, weight reduction.
I.
I NTRODUCTION
Now a days the fuel efficiency and emission gas regulation of automobiles are two important issues. To overcome this problem, the automobile industries are trying to make new vehicle which can provide high efficiency with low cost. The best way to increase the fuelefficiency is to reduce the weight of the automobile. The weight reduction can be achievedprimarily by the introduction of better material, design optimization and better manufacturingprocesses. The achievement of weight reduction with adequate improvement of mechanicalproperties has made composite a very good replacement material for conventional steel.
In automobile car, out of many components one of the components of automobile which canbe easily replaced is leaf spring. A leaf spring is a simple form of spring, commonly used forthe suspension in wheeled vehicles. The suspension of leaf spring is the area which needs tofocus to improve the suspensions of the vehicle for comfort ride. The suspension leaf springis one of the potential items for weight reduction in automobile as it accounts for 10 to 20%of unsprung weight[3].
It is well known that springs are designed to absorb shocks. So the strain energy of thematerial becomes a major factor in designing the springs. The introduction of compositematerial will make it possible to reduce the weight of the leaf spring without reduction in loadcarrying capacity and stiffness. The composite material have high strength to weightratio and have more elastic strain energy storage capacity as compared with steel.
It can be easily observed that material having lower density and modulus will have a greaterspecific strain energy capacity. Thus composite material offer high strength and light weight. The suspension quality can be improved by minimizingthe vertical vibrations, impacts and bumps due to road irregularities which create thecomfortable ride.
The automobile sector is introducing a number of cars which are newly designed, and modified by replacing some parts with advanced and composite materials for better comfort ride, lowweight and having better mechanical properties. India is a country with more than one billionpeople, require vehicle to move anywhere around the country for their personal andtransportation purpose. We have personally seen and observed that vehicle having nosmooth suspension or comfort ride create the tiredness to the people and more especially todrivers of car who is the life of passenger. Also, now a days so many passenger cars are availablewhich are employed for local transport around 200 to 300 km, aday with overloading of passengers which increase the total weight of the vehicle and alsoincrease the fuel consumption which leads to noise and breakage problem in the suspensionof leaf springs and create the pollution in the environment.
II.
LITERATURE REVIEW
Mahmood M. Shokrieh and DavoodRezaei [4] have worked on analysis and optimization of a composite leaf spring. In this work, they considered light vehicle rear suspension system with four-steel leaf spring for analysis of stress and deflection by using ANSYS V
5.4 software. Also they have compared the finite element result of stresses and deflection with existing analytical and experimental solution. After that using this result they have replaced steel leaf spring by
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International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016) composite material of fiberglass with epoxy resin and analysed it with same loading condition for stresses and deflection. Also from the analysis result they optimized spring geometry and found that spring width decreases hyperbolically and thickness increases linearly from spring eyes towards the axle seat.They concluded that the optimized composite leaf spring had much lower stress as compared to steel spring and thespring weight without eye units which in steel is 9.2 kg decreased by 80 % of itsvalue.
M.Venkatesan and D.Helmen [5] have worked on design and analysis of composite leaf spring in light vehicle. In their paper, they considered passenger cars with seven-leaf steel spring for analysis of stress and deflection by using ANSYS 10 software. The objective is to compare the load carrying capacity, stiffness and weight reduction of composite leaf spring with that of steel leaf spring. They compared the finite element analysis results of stresses and deflection with existing analytical and experimental results and replaced steel leaf spring by composite material of Eglass/Epoxy and analysed it with same loading condition for stresses and deflection. The dimensions and the number of leaves for both steel leaf spring and composite leaf springs are considered to be the same.
The design constraints were stresses and deflections.
They concluded that, the composite leaf spring exhibits 67.35% less stress, 64.95% higher stiffness and 126.98% higher natural frequency than that of existing steel leaf spring. A weight reduction of 76.4% is achieved by using optimized composite leaf spring.
Joo-teck Jeffrey and TarlochanFaris[6] have worked on Finite element analysis on the static and fatigue characteristics of composite multi-leaf spring. They investigated the static and fatigue behaviours of steel and composite leaf spring using the ANSYS V12 software. The dimensions of an existing conventional leaf spring of a light commercial vehicle were used.
The same dimensions were used to design composite leaf spring for the two materials, E-glass fibre/epoxy and E-glass fibre/vinyl ester, which are of great interest to the transportation industry. The design constraints were bending stresses, deflection and fatigue life. They concluded that, the maximum bending stresses and deflection in composite leaf spring are much lower than that of steel spring. The fatigue life of E-glass/epoxy or E-glass/ vinyl ester composite leaf spring was proven to be 2 and 4 times higher than that of steel leaf spring.
J.P. Hou, J.Y. Cherruault, I. Nairne, G.
Jeronimidis and R.M. Mayer[7] have worked on evolution of the eye-end design of a composite leaf spring for heavy axle loads. They considered freight rail applications with two leaf steel spring for analysis of stress and deflection by using FEA. They have compared the finite element analysis result of stresses and deflection with existing analytical and experimental solution. Using these results they have replaced steel leaf spring by composite material of glass reinforced polyester (GRP) and analysed it with same loading condition for stresses and deflection.
They concluded that, composite leaf spring have lesser stress, higher stiffness compared to steel leaf springand that composite leaf spring have very good fatigue life than that of existing steel leaf spring.
H.A. Al-Qureshi [8] has worked on automobile leaf springs from composite materials. The aim of this paper is to present a general study on the analysis, design and fabrication of composite springs. From this viewpoint, the suspension spring of a compact car, ``a jeep'' was selected as a prototype. A single leaf, variable thickness spring of glass fibre reinforced plastic (GFRP) with similar mechanical and geometrical properties to the multi leaf steel spring, was designed, fabricated and tested. The testing was performed experimentally in the laboratory and was followed by the road test. He concluded that, composite leaf spring have better fatigue behaviour than steel spring. Also he found the hybridization technique can be used effectively to improve weight saving and performance in the automotive industry.
Abdul Rahim Abu Talib, Aidy Ali, G. Goudah,
NurAzidaCheLah and A.F. Golestaneh[9] have worked on developing a composite based elliptic spring for automotive applications. They considered light and heavy trucks with steel elliptic spring for analysis of fatigue behaviour and weight reduction by using ANSYS software. The objective is to compare the load carrying capacity, fatigue behaviour and weight savings of composite leaf spring with that of steel leaf spring. They compared the finite element analysis result of fatigue life and weight reduction with existing analytical and experimental results.
Using these results they replaced steel leaf spring by composite material and analysed it with same loading condition. They concluded that composite elliptical springs have better fatigue behaviour than the conventional steel leaf spring and weight reduction ratio is achieved.
I. Rajendran and S. Vijayarangan [10] had studied about optimal design of a composite leaf spring using genetic algorithms-a powerful non-traditional optimization method. They considered automobile steel leaf spring for solution of fatigue failure and weight reduction by using genetic algorithms. Using results they replaced steel leaf spring by composite material and analysed it under same loading conditions. The dimensions and the number of leaves for both steel leaf spring and composite leaf springs are considered to be the same. Also from the result, they concluded that the composite leaf spring have very good fatigue life than that of existing steel leaf spring and weight reduction is achieved 75.6%.
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International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
Malaga. Anilkumar, T. N. Charyulu and Ch.
Ramesh[11] studied design optimization of leaf spring. They suggested to replace the multi-leaf steel spring by three types of composite leaf spring for the same load carrying capacity and stiffness. Since the composite materials have more elastic strain energy storage capacity and high strength-to-weight ratio as compared to those of steel, it is possible to reduce the weight of the leaf spring without any reduction in load carrying capacity and stiffness. The design constraints were limiting stresses and displacement. Modelling and analysis of both the steel and composite leaf springs have been done using ANSYS 9.0 software.
From the static analysis results, they saw that the vonmises stress in the steel is 596.047 MPa and the vonmises stress in E-glass/epoxy, Graphite/epoxy and
Carbon/epoxy is 475.606 MPa, 1556 MPa and 1061
MPa respectively. Composite leaf spring reduces the weight by 85% for E-Glass/Epoxy, 94.18% for
Graphite/Epoxy and 92.94 % for Carbon/Epoxy over conventional leaf spring.
M Senthil Kumar and S Vijayarangan[12] have worked on static analysis and fatigue life prediction of steel and composite leaf spring for light passenger vehicles. They described static and fatigue analysis of steel leaf spring and composite multi leaf spring using
ANSYS 7.1 software. Primary objective was to compare the load carrying capacity, stiffness and weight savings of composite leaf spring with that of steel leaf spring. They compared the analysis results with experimental results. They concluded that,
Composite leaf spring have 67.35% lesser stress,
64.95% higher stiffness and 126.98% higher natural frequency than that of existing steel leaf spring. They concluded that optimized steel leaf spring weight about 13.5 kg whereas the E-glass/Epoxy multi leaf spring weight only 4.3 kg, thereby weight reduction
(68.15%) is achieved and fatigue life of composite leaf spring (10, 00,000 cycles) was more than that of conventional steel leaf spring (2, 00,000 cycles).
III.
D ETAILS OF T EACHING
O
L EARNING
PTIMIZATION
B ASED
Teaching Learning Based Optimization was proposed by R.V. Rao et al in 2011. It is considered as a population based method as it uses a population of solutions in order to obtain the global solution. The population is considered as a “group of learners” or a
“class of learners”. The process of TLBO consists of two parts: the first part is the “teacher phase” and the second part is the “Learners phase”. The “teacher phase” means learner learns from the teacher and the
“Learners phase” means learner learns by the interaction between themselves.
The Basic philosophy of TLBO method is explained with the help of fig.3.1 and fig.3.2
Fig 3.1: Distribution of marks obtained by learners taught by two different teachers
[1]
Assume two different teachers T1 and T2 teaching the same content of a subject and to the same quality of learners in two different classes. Fig.4.1 shows the distribution of marks obtained by the learner of two different classes evaluated by the respective teacher.
Curves 1 and 2 represent the marks obtained by the learner in the subject taught by teacher T1 and T2 respectively. From fig.4.1, as we can see that curve 2 represents better result than curve 1, then in this case we can say that teacher T2 is better than teacher T1 in terms of teaching. The difference between both the result is nothing but the mean (i.e. M2 for curve 2 and
M1 for curve 1) i.e. a good teacher yield a better mean for the results of the learners.
Fig 3.2: Model for distribution of marks obtained for a group of learners
[1]
The teacher is considered as the most knowledgeable person the class, so the best learner acts as a teacher which is shown by TA in fig. 3.2. The teacher tries to share knowledge among learners, which will in turn increase the knowledge level of the whole class and help learners to get good marks or grades, thereby increasing the mean of the class. A teacher increases the mean of a class according to the quality of teaching delivered by a teacher and the quality of student present in the class. The quality of student is determined by the mean value of the population.
In fig. 3.2 Teacher TA puts effort so as to increase the mean from MA to MB at which stage the student require a new teacher of superior quality than themselves, i.e. in this case the new teacher is TB.
Hence, there will be a new curve-B with new teacher
TB. In the next sub section, teacher and learner phase are discussed.
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International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
Teacher phase:
From fig. 3.2 we see that the mean of a class increases from MA to MB depending upon a good teacher.
A good teacher is one who brings his or her learners up to his or her level in terms of knowledge. But in practice this is not possible and a teacher can only move the mean of a class up to some extent depending on the capability of the class.
Learners phase:
The learner can increase their marks by two ways, one is by getting explanation from the teacher and the other way is presentation, group discussion, interaction, communication with the other student. In this way a learner learns something new and extra, provided that the other learner has more knowledge than him or her.
TLBO Analogies e) The value of TF is selected as 1 or 2. The obtained difference is added to the current solution to update its value using f) X new
is accepted if it gives better function value.
Step 4: Learner phase
In this phase the learner increase the knowledge with interaction.
Step 5: Termination Criteria
If the maximum generation number is achieved, stop the algorithm or repeat from step 3.
IV.
OPTIMAL PROBLEM FORMULATION
Group of Students
Different subjects
Population
Different Design Variables
The purpose of the formulation is to create a mathematical model of the optimal design problem, which can be solved using an optimization algorithm.
Objective function
The objective is to minimize the weight of the leaf spring with the prescribed strength and stiffness. The objective function identified for the leaf spring problem is given below.
Result Score Fitness Value of the Problem
Teacher Best Solution
Fig 3.3: TLBO Analogies
Steps for implementing TLBO:
TLBO can be implemented easily, just by following the below steps:
Step 1: Define the optimization problem and initialize the optimization parameter. Initialize the population size, number of generationsand number of design variable and limit of design variables.
Step 2: Generate a random population as per the population size and the design variables. Population size denotes the no. of learners and the design variable denotes the subject. The population is expressed as,
, where is the material density, is the thickness at center, is the width at center and is the length of the leaf spring.
Design variables
A design problem usually involves many design parameters, of which some are highly sensitive.
These parameters are called design variables in the optimization procedure. In the present problem the following variables are considered (1) center width, and (2) center thickness,
Design parameters
Design parameter usually remains fixed in relation to design variables. Here the design parameters are length of leaf spring, , design load, material properties-(i) density, p, (ii) modules of
,
Step 3: Teacher phase: a) Calculate the mean of the population column wise, which will give the mean for the particular subject as, b) The best solution will act as teacher for that particular iteration. elasticity, and (iii) maximum allowable stress, .
Design constrains
Constrains represent some functional relationships between design variables and other design parameters.
Which satisfy certain physical phenomenon and resource limitations. In this problem the constraints are the bending stress, and vertical deflection, d.
(2) c) The teacher will try to move the mean from M
,D towards X teacher
which will act as a new mean from that iteration. d) The difference between two mean is expressed as
(3)
(4)
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International Conference on Global Trends in Engineering, Technology and Management (ICGTETM-2016)
When considering both static and fatigue behavior of composite leaf spring, the factor of safety (FOS) is taken as 2.5.
V.
C OMPUTER PROGRAM
5) The methodology facilitates to maximize the strength with minimum possible cross section dimensions.
6) Minimum number of leaves can be justified in the given application with due reduction in overall weight of the component. A tailor made computer program using MATLAB has been developed to perform the optimization process and to obtain the best possible design. The approach consists of minimising the weight of the leaf spring with required strength and stiffness. The flowchart describing the step by step procedure of optimising the composite leaf spring using Teaching Learning Based optimization (TLBO) is shown in figure no. 5.1.
Initialize number of students (population), termination criterion
R EFERENCES
[1] R.V.Rao, V.J. Savsani, D.P. Vakharia, “Teaching-learning based optimization: A novel method for constrained mechanical design optimization problems”, Computer aided design, Vol. 43, Issue 3,
2011, pp.303-315.
Reject
𝑋 𝑛𝑒𝑤
= 𝑋 𝑜𝑙𝑑
+ 𝑟𝑎𝑛𝑑(𝑋 𝑖
− 𝑋 𝑗
)
Reject
Calculate the mean of each design variables
Identify the best solution (teacher)
Modify solution based on best solution
𝑋 𝑛𝑒𝑤 ,𝐷
= 𝑋 𝑛𝑒𝑤 ,𝐷
+ 𝑟𝑎𝑛𝑑(0,1) 𝑋 𝑡𝑒𝑎𝑐 ℎ𝑒𝑟
− 𝑇 𝑓
𝑀
𝐷
No
Yes
No
Is new solution better than existing?
Select two solutions randomly X i
and X j
Is X i
is better than X j
?
Is new solution better than existing?
Yes
No
𝑋 𝑛𝑒𝑤
= 𝑋 𝑜𝑙𝑑
+ 𝑟𝑎𝑛𝑑(𝑋 𝑗
− 𝑋 𝑖
)
Yes
Accept
Accept
No
Is termination criteria satisfied?
Yes
Final value of solution
Fig 5.1: Flow chart for Teaching-Learning-Based
Optimization (TLBO) [1]
[2] Osama J. Aldraihem, Tarunraj Singh and Robert C. Wetherhold,
“Optimal size and location of piezoelectric actuator/sensor: practical consideration”, journal of guidance, control and dynamics, 2000, pp.
509-515
[3]Tanabe K, Seino T, Kajio Y. characteristics of carbon/glass fibre reinforced plastic leaf spring. SAE 820403. 1982, p.1628-34
[4]Mahmood M. Shokrieh, DavoodRezaei, “Analysis and optimization of a compositeleaf spring”, Composite Structures 60
(2003) 317–325.
[5] M.Venkatesan, D.Helmen
,
“Design and analysis of composite leaf spring in lightvehicle”, International Journal of Modern
Engineering Research, Vol.2, Issue.1, 2012,pp 213-218.
[6] Joo-teck Jeffrey, TarlochanFaris, “Finite element analysis on the static and fatiguecharacteristics of composite multi-leaf spring”,
Journal of Zhejiang University-Science, Vol. 13, 2012, pp 195-164
[7] J.P. Hou, J.Y. Cherruault, I. Nairne, G. Jeronimidis, R.M. Mayer,
“Evolution of theeye-end design of a composite leaf spring for heavy axle loads”, Composite Structures78 (2007) 351–358.
[8]H.A. Al-Qureshi, “Automobile leaf springs from composite materials”, Journal ofMaterials Processing Technology, 118, 2001,
58-61.
[9]Abdul Rahim Abu Talib, Aidy Ali, G. Goudah, NurAzidaCheLah,
A.F. Golestaneh,“Developing a composite based elliptic spring for automotive applications”, Materialsand Design, 31, 2010, 475–484.
[10]I. Rajendran, S. Vijayarangan, “Optimal design of a composite leaf spring usinggenetic algorithms”, Computers and Structures, 79,
2001, 1121-1129.
[11]Malaga. Anilkumar, T. N. Charyulu, Ch. Ramesh, “Design
Optimization of LeafSpring”, International Journal of Engineering
Research and Applications, Vol. 2,Issue 6, 2012, pp.759-765.
[12]M. Senthil Kumar, SVijayarangan, “Static analysis and fatigue life prediction of steeland composite leaf spring for light passenger vehicles”, Journal of Scientific &Industrial Research, Vol. 66, 2007, pp 128-134.
VI.
CONCLUSION
1) The review study shows that composite leaf spring is useful for reduction of weight as well as economical as compared to conventional leaf spring with the same parameters.
2) The composite leaf spring have much lower stresses and deflection and higher fatigue life.
3) The design of composite leaf spring can enable replacement of seven-leaf steel spring of an automobile with a mono-leaf composite spring.
4)In this review paper, we have discussed that the design variables (leaf thickness and width) of steel and composite leaf springs are optimized by making use of
TLBO: a novel optimization method.
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