Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 Modeling and Analysis of Aluminum A360 Alloy Helical Gear for Marine Applicaions B.Venkaesh 1, V.Kamala A.M.K.Prasad 3 1 Associae Professor, MED, Vardhaman College of Engg, Hyderabad, India Professor, MED, MJCET, Hyderabad; DGM (Red), BHEL R&D, Hyderabad, India 3 Professor, & Head, MED, Osmania college of Engg, Osmania Universiy, Hyderabad, India bv_75@yahoo.co.in Absrac Gears are one of he mos criical componens in mechanical power ransmission sysems. Today s compeiive business in he global marke has brough increasing awareness o opimize he gear design. The gears are generally used o ransmi power or orque and he efficiency of ransmission is very high when compared o oher kind of ransmissions. The helical gear offers high conac and more fricion which avoids slippage when compared o spur gear. To esimae he bending sress, hree dimensional solid models for differen number of eeh are generaed by CATIA ha is powerful and modern modeling sofware and he numerical soluion is done by ANSYS, which is a finie elemen analysis package. The analyical invesigaion is based on Lewis sress formula. The aim of he presen sudy is o focus on reducion of weigh and here by reducing he unbalance forces seup in he sysem. Key words: Gear design, Compuer aided analysis, high speed helical gear, dynamic analysis 1. Inroducion The moion from one shaf o anoher shaf may be ransmied wih bels, ropes and chains. These mehods are mosly used when he wo shafs are having long cener disance. Bu if he disance beween he wo shafs is very small, hen gears are used o ransmi moion from one shaf o anoher. In case of bels and ropes, he drive is no posiive. There is slip and creep ha reduces velociy raio. Bu gear drive is a posiive and smooh drive, which ransmi velociy raio. Gears are used in many fields and under a wide range of condiions such as in smaller waches and insrumens o he heavies and mos powerful machineries like lifing cranes. Gears are mos commonly used for power ransmission in all he modern devices. These oohed wheels are used o change he speed or power beween wo sages (inpu and oupu). They have gained wide range of accepance in all kinds of applicaions and have been used exensively in he high speed marine engines. In he presen era of sophisicaed echnology, gear design has evolved o a high degree of perfecion. The design and manufacure of precision cu gears, made from maerials of high srengh, have made i possible o produce gears which are capable of ransmiing exremely large loads a exremely high circumferenial speeds wih very lile noise, vibraion and oher undesirable aspecs of gear drives. Helical gears are he modified form of spur gears, in which all he eeh are cu a a consan angle, known as helix angle, o he axis of he gear, where as in spur gear, eeh are cu parallel o he axis. Helical gears are also employed o ransmi power beween wo shafs parallel o he axis. The following are he requiremens ha mus be me in he design of gear drive. The gear eeh should have sufficien srengh, so ha hey will no fail under saic and dynamic loading during normal running condiions. The gear eeh should have clear characerisics so ha heir life is saisfacory, he use of space and maerial should be economical. The alignmen of he gears and 14
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 deflecions of he Shafs mus be considered, because hey affec he Performance of he gears. The lubricaions of he gears mus be saisfacory. Currenly he popular sandards are ISO and AGMA. These sandards vary in seleced approaches as well as models and mehods resuling in differen design soluions obained for he same gear under he same se of working condiions. Gear ransmissions affec energy consumpion during usage, vibraion, noise and warrany coss among ohers facors. These facors are criical in modern compeiive, manufacuring, especially in he aviaion indusry which demands excepional operaions requiremens concerning high reliabiliy and srengh, low weigh and energy consumpion, low vibraions and noise. Considering heir reliabiliy and efficiency are some of he mos imporan facors, problems of disribuions of loads and consequenly, disribuion of sresses in he whole gear ransmission, paricularly in eeh of maing gears, need o be horoughly analyzed. Gear ransmissions are widely used in various indusries and heir efficiency and reliabiliy are criical in he final produc performance evaluaion.. Design mehodology.1 Gear design based on AGMA Procedure: The design of helical gear is almos similar o spur gear design wih sligh modificaions in Lewis and Buckingham equaions due o helix angle. According o Lewis equaion, he beam srengh of helical gear ooh is given by b [ σ ] b b π m n y v σ, Where [ b ]Allowable conac sress in N/mm,bace widh of gear blank 10 m n, M n Normal module which mus be sandardized., y v Lewis form facor which depends on he Z 3 virual number of eeh Z v Cos β, or safe working, he beam srengh should be greaer han he design ooh load K s C v D K s C v D which is given by v, The values of K a, C v, v ec., are calculaed similar o spur gears. The dynamic load acing on helical gear ooh may be found ou using 1 v ( Cb cos β + ) cos β d + 1 v + Cb cos β + Buckingham equaion as and he wear ooh load is given by d 1 b Q K w w Cos β The values of Q and K w ec., are all common wih spur gears. The design procedure is also very similar o spur gears. 3. Resuls and discussion 3.1 Theoreical design calculaions Here he heoreical calculaions for design are performed by using he inpu parameers such as power for marine high speed engine P9000KW, speed of he pinion 3500 rpm, gear raio 7 and helix angle β 5 0 Minimum cener disance based on surface compression srengh is given by a ( 7 + 1 ) 3 0. 7 σ c E [ M ] x i ψ [Table 8, PSG] 15
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 Calculaions for aluminum alloy [98%Al O 3, 0.4 0.7%Mn, 0.4 0.7&Mg] Maerial Selecion: Le he maerial for Pinion & Gear is Aluminum Alloy. Is design compressive sress & bending sresses are [σc 5000 kgf/cm], [σb 3500 kgf/cm] [17] Properies for Aluminum Alloy: Densiy of Aluminum Alloy (ρ) 3900 kg/m 3 Young s Modulus 340 x 103 N/mm,Poisson s Raio (v) 0.0,i 7,ψ 0.3, [Table 9, 10 PSG ] [MT] MT k d k,mt 9740 KW/N k d k 1.3,[MT] MT kdk (9740 x 9000x1.3)/3500 35661 kgf cm Now, minimum cenre disance based on he surface compressive srengh is given by 0.7 (i + 1)x 3 xe [ M ] σ c a ( i ψ ) a > 59.59 cm 60 cm Minimum module based on beam srengh: Mn > 1.15cosβx{ [M ]/(Y v σb Ψ m Z 1 ) 1/3 } [Table 8, PSG ] Le Z1 18, ψm 10[Table 11, PSG 8.14] Virual number of eeh Z v Z 1 /cos β 18/0.744 5 Lewis form facor Yv (for Zv 5) 0.405 m n > 1.15cos5x{ 35661.14/(0.405x3500x10x18)} 1/3 > 1.11 cm, m n > 11.16 mm Bu for mn 11 16 mm, σc and σb are > [σc] & [σb] also S < D which makes design unsafe. So m n 18 mm 1.8 cm, No. of eeh of pinion, Z1 (a cos β )/ m n (i+1) 1 Bu in order o avoid inerference, Z 1 is aken as 18, No. of eeh on gear, Z iz 1 16 Diameer of he pinion (m n xz 1 )/cos β (1.6x18)/cos 5 35.74cm Diameer of he gear (d ) I d 1 7 x 35.74 50.4 cm, Cener disance (a) (d 1 +d )/ 14.99cm ace widh b ψ.a 0.3 x 14.99 43 cm Checking Calculaions: σc 0.7x i + 1 a i + 1 xe [ M ib ] [ σ ] c σb 0.7x {(i+1)/(a.b.m n.y v )}[M ] [σc] Based on he Compressive Sresses: σc (0.7x8x35661.14)/(88.4x43x0.405) 8.35 N/mm 16
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 Based on he bending sress σb 178.59 N/mm from he calculaions, σc and σb are [σc] & [σb] values of given maerials, Therefore our design is safe. Addendum, m n 18 mm, Dedendum 1.5 x m n.5 mm, Tip circle diameer of he pinion d1 + ( x addendum) 357.4 + 3.6 393 mm Tip circle diameer of gear d + ( x addendum) 50 + 3.6 538 mm Roo circle diameer of pinion d1 ( x addendum) 357.4 3.6 31.4 mm Roo circle diameer of gear d ( x addendum) 50 3.6 466 mm When he gear ransmis he power P, he angenial force produced due o he power is given by (Pxk s )/v 3 π xd p xn p π x 357. 4 x 3500 9000 x 10 x V 65. 4 m / s 75145. 1 N 60 x 1000 60 x 1000, 65. 4 Lewis derived he equaion for beam srengh assuming he load o be saic when he gear is running a high speeds, he gears may be subjeced o dynamic effec. To accoun for he dynamic effec, a facor Cv known as Velociy facor or dynamic facor is considered. The design angenial force along wih dynamic effec is given by Pxk s xcv xcv D V The velociy facor Cv is developed by Barh. I depends on he pich line velociy and he workmanship in he manufacure and is is given by C v (5.5 + v 1/ ) / 5.5 for V > 0 m/s. Where 75145.1 N, Ks, V 65.4 m/s, 5. 5 + 65. 4 C v. 47 5. 5 D 75.145 x.47 679771.90 N According o Lewis equaion, he beam srengh of helical gear ooh is given by S [σb].b.π.m n.yv (1.75 x 341) x 430 x П x 18 x 0.405 6101677.663 N (or) S [σb].b.π.m n.yv 4000 x 43 x π x 1.5 x 0.405 4089938.94 N Since, S > D, Our design is safe. When he power is ransmied hrough gears, apar from saic (seady) load produced by he power, some dynamic loads are also applied on he gear ooh due o reasons like inaccuracies of ooh profiles and deflecions of ooh under load. Considering he above condiions Buckingham desired an equaion o find ou he maximum load acing on he gear ooh which is given by d + i where d Maximum dynamic load, Saic load produced by he power,i Incremenal load due o dynamic acion Incremenal load depends on he pich line velociy, face widh, of a gear ooh, gear maerials, accuracy of cu and he angenial load and is is given by 0. 164 V ( cb cos β + ) Cos β m i 0. 164 V + 1 m. 485 cb cos β + Where, Vm Pich line velociy in m/s, b ace widh of he gear ooh in mm C Dynamic facor (or) Deformaion facor in N/mm. [17] Here, C 11860 x e, C 11860 x 0.06 308.36 N/mm, 13757.60 N, 17
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 Vm 65.4 m/s 65.4 x 103 mm/sec, b 38.16 cm 381.6 mm, 0. 164 V m ( cb cos β + b ) Cos β d + 0. 164 V + 1. 485 cb cos β + d m 13757. 60 + 0. 164 x 65. 4 0. 164 x 65. 4 39654. 95 747. 98 x + ( 1. 485 ( 308. 36 x 430 x cos d 13757. 60 + 140776. 6 N Since s > d, our design is safe. 308. 36 x 430 x cos 5 + 13757. 60 ) Cos 5 5 + 13757. 60 ) β 5 0, d + i One of he mos predominan gear failures is he failure of gear ooh due o piing. This piing failure occurs when he conac sresses beween he wo meshing eeh exceed he surface endurance srengh of he maerial. In order o avoid his ype of failure he proporions of gear ooh and he surface properies such as surface hardness should be seleced in such a way ha he wear srengh of he gear ooh is more han he effecive load beween he meshing eeh. Based on Herz heory of conac sresses, Buckingham derived an equaion for wear srengh of gear ooh which is given by w (d 1.b.Q.Kw)/ cos β, Where; w Max or limiing load for wear in Newons, d1 Pich circle diameer of pinion in mm,b ace widh of he pinion in mm Q Raio facor i /(i+1) 1.75,Kw.553 N/mm [Table 5.37 JDB] d 1.b.Q.Kw d 1 357.4mm,b 430 mm, w cos β w 357.4x430x1.75x.553/cos 5 900086.75N, d 140776.6 N Since w > d our design in safe. 3. Solid Modeling and EM Package Solid Modeling is geomerical represenaion of a real objec wihou losing informaion he real objec would have. I has volume and herefore, if some one provides a value for densiy of he maerial, i will have mass and ineria. Unlike he surface model, if one makes a hole or cu in a solid model, a new surface is auomaically creaed and he model recognizes which side of he surface is solid maerial. The mos useful hing abou solid modeling is ha i is impossible o creae a compuer model ha is ambiguous or physically non realizable.a model is creaed using CATIA sofware and hen i is rerieved ino ANSYS using IGES files. The proporions of gear coming ou from heoreical design and which are used o creae he model. 3.3 Analysis Significan Developmen in analysis of srengh properies of gear ransmission follows he achievemens in compuaion design, simulaion of meshing and ooh conac analysis made by Lewiki,Handschuh.They carried ou D analyses using finie elemen mehod, boundary elemen mehods & Compared he resuls o experimenal ones validaed crack simulaion based on calculaed sress inensiy facors and mixed mode crack angle predicion. In pracice, simplified formulas are usually used in gear ransmission design. They enables esimaion of sresses a ooh roo wih accuracy accepable for engineering design. In every case, srengh properies of gear ransmissions are srongly influenced by gear geomery, applied manufacuring processes, and dimensional accuracy of manufacured gears. 18
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 3.3.1 Vibraion analysis I is used o es he maerial agains random vibraions, shock and impac. Each of he incidens may ac on he naural vibraion frequency of he maerial, which in urn, may cause resonance and subsequence failure. 3.3.1. Modal analysis: I is he applicaion of he EM, used o deermine he vibraion characerisics (naural frequencies and mode shapes) of a srucure of a machine componen while i is being designed. The naural frequencies and mode shapes are imporan parameers in he design of a srucure for dynamic loading condiions. Modal analysis is he ANSYS family of producs and i is a linear analysis. Any nonlineariy, such as Plasiciy and conac (gap) elemens are ignored even if hey are defined. You can choose from several mode exracion mehods: subspace, Block Lanczos, power Dynamics, reduced, unsymmerical, and damped. The damped mehod allows you o include dampin in he srucure. igure 3.1: Von misses sress for Aluminum alloy igure 3.: Mode shape1 for Aluminum alloy 19
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 igure 3.3: Mode shape for Aluminium Alloy igure 3.4: Mode shape 3 for Aluminium Alloy igure 3.5: Mode shape 4 for Aluminium Alloy 130
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 igure 3.6: Mode shape 5 for Aluminium Alloy igure 3.7: Mode shape 6 for Aluminium Alloy igure 3.8: Mode shape 7 for Aluminium Alloy 131
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 igure 3.9: Mode shape 8 for Aluminium Alloy igure 3.10: Mode shape 9 for Aluminium Alloy igure 3.11: Mode shape 10 for Aluminium Alloy The Table 3.1 & graph shows he modal analysis for aluminum alloys 13
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 Table 3.1: Modal analysis for Aluminium alloys requency Displacemen 6500 4.81 8507 7.41 9535 7.33 9661 7.373 9954 6.1 10057 6.6 1084 6.711 1094 9.538 1096 9.854 1657 8.96 3.3.1. Modal analysis: I is he applicaion of he EM, used o deermine he vibraion characerisics (naural frequencies and mode shapes) of a srucure of a machine componen while i is being designed. The naural frequencies and mode shapes are imporan parameers in he design of a srucure for dynamic loading condiions. Modal analysis is he ANSYS family of producs and i is a linear analysis. Any nonlineariy, such as Plasiciy and conac (gap) elemens are ignored even if hey are defined. You can choose from several mode exracion mehods: subspace, Block Lanczos, power Dynamics, reduced, unsymmerical, and damped. The damped mehod allows you o include damping in he srucure. 4. Conclusions 1. Von misses sress was obained by heoreical and Ansys sofware for Aluminum alloy, values obained from ANSYS are less han ha of he heoreical calculaions.. The naural frequencies and mode shapes are imporan parameers in he design of a srucure for dynamic loading condiions, which are safe and less han he oher maerials like seel. 3. Aluminum alloy reduces he weigh up o 55 67% compared o he oher maerials 4. Aluminum is having unique propery (i.e. corrosive resisance), good surface finishing, hence i permis excellen silen operaion. 5. Weigh reducion is a very imporan crierion, in order o minimize he un balanced forces seup in he marine gear sysem, here by improves he sysem performance. 133
Volume 1, No, 010 Copyrigh 010 All righs reserved Inegraed Publishing Associaion RESEARCH ARTICLE ISSN 0976 459 Graph Displacem en Vs requency 14000 1000 10000 8000 6000 Series1 Series 4000 000 0 1 3 4 5 6 7 8 9 10 D isp lacemen igure 3.11: Graph showing Modal analysis for Aluminium alloy 6. Hence aluminum alloy is bes suied for marine gear in he high speed applicaions. 7. As a fuure work, harmonic and ransien analysis of he gear can be performed o find ou he effec of various cyclic loading condiions along wih emperaure variaions. Acknowledgemens irs auhor is graeful o Dr.T.Srinivasulu, Principal VCE shamshabad and Dr.G.V.Rao Head Mechanical Engineering Deparmen for heir valuable suppor. He is also hankful o he managemen of he insiue for he encouragemen, suppor, and co operaion during he enire work. 5. References 1. J.O.Nordiana, S.O.Ogbeide, N.N.Ehigiamusoe and.i.anyasi., 007, Compuer aided design of a spur gear, Journal of Engineering and Applied Sciences (1); pp 1743 1747.. Zeping Wei., 004 Sresses and Deformaions in Involue spur gears by inie Elemen mehod, M.S, Thesis, College of Graduae Sudies and research, Universiy of Saskachewan, Saskachewan. 3. Darle W.Dudley, 1954, Hand book of pracical gear design 4. Alec srokes, 1970, High performance of gear design 5. Maira, G.M, 004, Hand Book of Gear Design, TaaMcGraw Hill, New Delhi.. 6. S.Md.Jalaluddin., 006, Machine Design, Anuradha publicaions, Chennai. 7. Thirupahi Chandrupala, Ashok D.Belegundu, Inroducion o finie elemen in Engineering, 003 8. PSG, 008. Design daa, Kalaikahir Achchagam publishers, Coimbaore, India. 9. S.Mahalingam, R.E.D Bishop, 1974, Dynamic loading of Gear ooh, Journal of sound and vibraion, 36(), pp179 189 10. S.H.Choi, J.Glienicke, D.C.Han, K.Urlichs, April 1999, Dynamic Gear Loads due o coupled laeral, Torsional and Axial Vibraions in a helical Geared Sysem, Journal of vibraion and acousics, Vol 11 /141. 134