Optimization of Flywheel Weight using Genetic Algorithm

Transcription

1 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March 0 Optiization o Flywheel Weight using Genetic Algorith A. G. Appala Naidu*, B. T.N. Charyulu, C..C.V.aanaurthy Naidu, D.M.atyanarayana Abstract: Optiization is a technique through which better results are obtained under certain circustances. The present work deals with the proble o weight iniization o lywheel. Flywheel proble has large nuber o ultivariable and non-linear equations / in equalities. Hence traditional optiization techniques cannot be applied in these cases. Traditional optiization techniques have a possibility or the solutions to get trapped into local inia. Also the algorith developed or one type o proble ay not be suitable or another type o proble. In this paper, a non traditional optiization technique, naely Genetic Algorith is used. Optial design o lywheel is solved using Genetic algorith. eywords: Optiization, Flywheel, Genetic Algorith, Weight. A. oll No.0A0D50, M.Tech Machine design, Dept. o Mechanical Engineering, Nova college o engineering, Jangareddygude, A.P Corresponding author, B. Associate Proessor, Departent o Mechanical Engineering, Nova College o engineering, Jangareddygude, A.P C. Proessor, Departent o Mechanical Engineering, HIT, Guntur, A.P D. oll No.0A0D505, M.Tech CAD/CAM Departent o Mechanical Engineering, Nova College o engineering, Jangareddygude, A.P. Introduction Design optiization can be deined as the process o inding the axiu or iniu o soe paraeters which ay call the objective unction and it ust also satisy a certain set o speciied requireents called constraints. Many ethods have been developed and are in use or design optiization. All these ethods use atheatical prograing techniques or solutions. In these cases it is diicult to apply traditional optiization techniques. Nonconventional techniques are applied to such cases. These are potential search and optiization techniques or coplex engineering probles. Genetic algoriths are ound to have a better global perspective than the traditional ethods. Dr. hapour Azar [, ] has worked on optiization o helical spring using consol-optcad and he extended his work to ly wheel using the sae optiization procedure..vijayarangan, V.Alagappan [] was applied Genetic Algorith technique or achine coponent i.e. Lea spring. By using Genetic Algorith, the optiu diensions o the lea spring were ound to be iniu weight with adequate strength and stiness. alyanoy Deb [5] presented dierent types o optiization algoriths viz., traditional and non-traditional algoriths. Genetic and All ights eserved 0 IJET 676

2 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March 0 siulated annealing algoriths were explained with exaples in non traditional algoriths. Genetic Algoriths have good potential as optiization techniques or coplex probles and have been successully applied in the area o Mechanical Engineering. Popular applications include achine eleents design, heat transer, scheduling, vehicle routing, etc.. Optial Proble Forulation The objectives in a design proble and the associated design paraeters vary ro product to product. Dierent techniques are to be used in dierent probles. The purpose o the orulation procedure is to create a atheatical odel o the optial design proble, which then can be solved using an optiization algorith. An optiization algorith accepts an optiization proble only in a particular orat. Figure show the coon steps involved in an optial design orulation process. The irst step is to realize the need or using optiization or a speciic design proble. Then the designer needs to choose the iportant design variables associated with the design proble. The orulation o optial design probles requires other considerations such as constraints, objective unction, and variable bounds. Usually a hierarchy is ollowed in the optial design process, although one consideration ay get inluenced by the other. Fig. Flow chart or general Optial design Procedure... Design variables and Constraints: The orulation o an optiization proble begins with identiying the underlying design variables, which are priarily varied during the optiization process. Other design paraeters usually reain ixed or vary in relation to the design variables. The constraints represent soe-unctional relationships aong the design variables and other design paraeters satisying certain physical phenoenon and certain resource liitations. oe o these considerations require that the design reain in static or dynaic equilibriu. In any echanical engineering probles, the constraints are orulated to satisy stress and delection liitations. Oten, a coponent needs to be designed in such a way that it can be placed inside a ixed housing, there by restricting size o the coponent. The nature and nuber o All ights eserved 0 IJET 677

3 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March 0 constraints to be included in the orulation depend on the user. There are usually two types o constraints that eerge ro ost considerations. Either the constraints are o an inequality type or o an equality type... Objective unction and Variable bounds: The coon engineering objectives involve iniization o overall cost o anuacturing or iniization o overall weight o a coponent or axiization o net proit earned or axiization o total lie o a product or others. Instead the designer chooses the ost iportant objective as the objective unction o the optiization proble and the other objectives are included as constraints by restricting their values with in a certain range. The objective unction can be o two types. Either the objective unction is to be axiized or iniized. The inal task o the orulation procedure is to set the iniu and the axiu bounds on each design variable. Certain Optiization algoriths do not require this inoration. In these probles, the constraints copletely surround the easible region. In general, all N design variables are restricted to lie with in the iniu and the axiu bounds as ollows: X i (L) X i X i (U). Optiization Proble Forat: The optiization proble can be atheatically written in a special orat, known as nonlinear prograing orat. Denoting the design variables as a colun vector X= (x l, x,.., x N ) T, the objective unction as a scalar quantity (X), J, inequality constraints as g j (X) 0, and k equality constraints and h (X)=0; Matheatical representation o the nonlinear prograing proble: Miniize (X) ubject to g j (X) 0, j=,,,j; h (X)=0, k=,,,; X i (L) X i X i (U), i =l,,.,n; The constraints ust be written in a way so that the right side o the inequality or equality sign is zero...optiization Algoriths. Certain probles involve linear ters or constraints and objective unction but certain other probles involve nonlinear ters or the. oe algoriths peror better on one proble, but ay peror poorly on other probles. That is why the optiization literature contains a large nuber o algoriths, each suitable to solve a particular type o proble. The optiization algoriths involve repetitive application o certain procedures they or i =, N. need to be used with the help o a coputer. In any given proble the.. Working Principle. deterination o the variables bounds When the siple Genetic Algoriths is X (L) i and X (U) i ay be diicult. One way to ipleented it is usually done in a anner that reedy this situation is to ake a guess about the involves the ollowing operators such as itness optial solution and set the iniu and proportionate,reproduction, crossover and axiu bounds so that the optial solution lies within these two bounds. The chosen bound ay not be correct. The chosen bound ay be readjusted and the optiization algorith ay be siulated again. utation. The Genetic Algorith begins with an initial population o size is equal to 0 (zeroth generation) o strings which consists o binary coding selected at rando. Thereater convert the binary coding in to decial value and calculate the actual values o design variables with in their range All ights eserved 0 IJET 678

4 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March 0 by using apping rule. Next calculates the value o objective unction by substituting the design variables and thereater violation coeicient (C) and the corresponding odiied objective unction is obtained. This odiied objective unction is used to calculate the itness values o each individual string and also calculate the average itness value. First, the reproduction operator akes a atch o two individual strings or ating, and then crossover site is selected at rando with in the string length and position values are swapped between the sae strings. Finally the utation is applied to the randoly selected strings. It is the rando lipping o the bits or gene that is changing a zero to one and vice versa, so that the irst cycle o operation is copleted which is called as iteration. This iteration is tered as generation in genetic Algoriths. This new generation creates a second population (i.e. generation -). This second population is urther evaluated and tested or optial solution which is obtained at zero violation Fig.. Flow chart o Genetic algorith 4. Optial Design o Flywheel. 4. Introduction It is widely used as an energy storage echanis in today's world. It is econoic because the growing costs and potential scarcity o energy have increased the iportance o energy and at the higher itness value. Genetic storage as a conservation easure and is algorith is a population based search and technological because iproveents in aterials optiization technique. It is an iterative ake lywheel energy storage ore attractive. optiization procedure. Genetic algorith works as ollows A punch press is one o those echanical systes in which a lywheel is used not only or power conservation but also as a echanical iltering eleent in a circuit through which power is lowing. In act, energy is stored in a lywheel by speeding it up and is delivered to it by slowing it down. It also acts as a soothing or equalizing eleent. Thereore a lywheel plays an iportant role in the perorance o the punch press. All ights eserved 0 IJET 679

5 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March 0 b h DIH DOH Fig.. Flywheel in Punch press. 4. Objective Function The objective unction is to iniize the weight o the lywheel (W F ) which is the su o the weights o ri (W ), hub (W H ) and spokes (W ). = W F = W+W H + s.ws The objective unction is sipliied by considering the weight o hub and spokes to be one-eighth o the weight o the ri concentrated at the ean radius o the ri. W H + s.w s = 8 W At point C, only torsional stress due to punching is taken into account. Presuably this stress is uch larger than any other stress present at point C, with proper overload actor. The torque producing this stress is given by T = F F ax = F cos sin sin Fax 0. 5 d t p up n OL Notice that point C is in act under partial (hal-cycle) torsional stress due to punching. Thereore the ean ( ( a ) shear stresses are considered as a ax ) and alternating Thereore the sipliied objective unction is W F = 8 9 W = 8 9 ( r h b )g c 4. Constraints 4.. Weight elation (g l ) The weight o the hub and spokes are one eight o the ri weight. (D OH -D IH )b H + ks d s (D I -D OH ) = r h b D I = r - h 4.. hat tress (g): T = T ince 6T ax D a us IH, Thus atigue is the governing criterion ns us a This constraint ay be written in the ollowing or ater sipliication D IH > ys 4T U n 4.. ey tress (g ): Fig.4. Torsional stresses A F k ax All ights eserved 0 IJET 680

6 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March 0 ak Thus F T and A = b H t k k τ D IH k ak ns k us ax key This constraint ay be sipliied to T t key k us 4..4 Energy o Flywheel (g4): ns b H D IH In order to ind the energy o the lywheel, irst ind the total energy which is used per stroke. 4 r - h - b -, 4 9 C E 4g 4..5 i stresses (g 5 ):- c N 60 The ri stresses have been developed due to cobined eect o hoop tension and bending stresses. The ri is subject to high bending stresses. The axiu cobined stress at the ri o the lywheel having six spokes is given by = 4. r h V V=ω. r and ω = N 60 The kinetic energy (.E) o a body rotating about a ixed center is.e I ince there is velocity change due to punching, the expression or change o energy is.e I( ax This ay be rewritten as.e I V ave r C in V ax - V in C, V ave V ax - V in V ave And c W r I, V= r g Thus the energy constraint is E E This can be written in the ollowing or ) D O = r + h Thereore u / 4..6 pokes tresses (g 6 ):- In the design o spokes, it is assued that cantilever action is predoinant. The bending oent due to punching at the hub o the ars is taken to be T(DO - D M s D For which the bending stress is k s d Z s O OH ) M where, Z It is sae to assue that each ar is in tension due to one-hal o the centriugal orce o that portion o the ri which it supports. 4 V, V= r Thereore + u s All ights eserved 0 IJET 68

7 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March ability (g7):- The hub length o the lywheel is usually taken greater than the shat diaeter or stability reasons. 5. esults and Discussions Optial design o lywheel has been D IH b H discussed by using Consol-Optcad and Optial Design Model Matheatical odel or optial design o optiization capability o Genetic Algoriths (GA). lywheel is suarized as Miniize even design variables and seven W F 9 ( r h 8 b ) g c ubject to table A. It was observed that the optiu diensions and iniu weight obtained by GA g :(D OH -D IH )b H + ks d s (r -h -D OH )- r h b = 0, g : D D b g : IH 4 g 4 :, g 5 : r h g 6 : + b s IH H u u DIH, g 7 : b The design variables r, h, b, D OH, D IH, b H and d s are the diensions o the lywheel. H constraints are considered in the lywheel proble. The results obtained or lywheel are shown in are better than the values obtained by the Consol- Optcad ethod. Method r ( h b D OH D IH b H d W (N) Consol Opt cad G.A The iniu weight o Flywheel obtained by GA is reduced by 4.5 %, when copared to the weight obtained by Consol - Optcad solution. 6.Conclusions:. Operation in Engineering Design is the past aied at a Design proble with single objective unction with single variable and with or without constraints. But here the code is used or the optiization o lywheel to iniize the weight. It is ound that the results obtained by genetic algoriths are better, search space is wide and it ais at global optiu than that the local All ights eserved 0 IJET 68

8 IN: International Journal o cience, Engineering and Technology esearch (IJET) Volue, Issue, March 0 optiu as in a traditional ethod or the sae input paraeters. It is ound that the results obtained ro genetic algoriths are less in weight as copared to consol opticad ethod. 7. eerence. Dr.hapour Azar, 996, "Flywheel optiization via consol-optcad", University o Maryland, UA.. Dr.hapour Azar, 996, "Helical copression spring Optiization via Consoloptcad", University o Maryland, UA...Vijayarangan, V.Alagappan, I.ajendran, 999, "Design optiization o Lea prings using Genetic Algoriths", Journal o IE (I), vol 70 pp: David E.Goldberg., 989, "Genetic Algoriths in search optiization a Machine learning", Addison-Wesley publishing copany, ingapore. 5. alylanoy Deb., 995, "Optiization or Engineering Design Algoriths and Exaples", Prentice-Hall o India Private Liited, New Delhi. 6. ingiresu..ao., 984, "Optiization Theory and applications", Wiley Eastern, New Delhi. All ights eserved 0 IJET 68