EFFECT OF STRESS RELIEVING FEATURES ON STRESSES OF INVOLUTE SPUR GEAR UNDER STATIC LOADING

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1 Inernaional Journal of Emerging Technology and Innovaive Engineering Volume I, Issue 5, May 015 (ISSN: ) EFFECT OF STRESS RELIEVING FEATURES ON STRESSES OF INVOLUTE SPUR GEAR UNDER STATIC LOADING Sarfraz Ali N. Quadri M.E. (CAD/CAM) Deparmen of Mechanical Engineering MGM s Jawaharlala Nehru Engineering College, Aurangaad (M.S.), India sarfrazaliquadri@gmail.com Dhananjay R. Dolas Associae Professor Deparmen of Mechanical Engineering MGM s Jawaharlal Nehru Engineering College, Aurangaad (M.S.), India dhananjay_dolas@rediffmail.com ABSTRACT This work made an aemp o summarize aou sresses developed in a maing spur gear which has involue eeh. A pair of spur gears are aken from a lahe gear ox and progressed onward o calculae sresses in heir eeh. Convenionally he analysis is carried ou analyically using Lewis formulae and hen Finie Elemen Analysis is used for he same. In his sudy some sress reliving feaures have een incorporaed in he eeh o know heir effec on he sress concenraions. A finie elemen model of eeh is considered for analysis and geomerical feaures of various sizes are inroduced a various locaions and heir effec is analyzed. Keywords Sress Analysis, Involue spur gear, saic loading, Lewis formulae, Sress relieving feaures. 1. INTRODUCTION Gears are used for a wide range of indusrial applicaions. They have varied applicaion saring from exile looms o aviaion indusries. They are he mos common means of ransmiing power. They change he rae of roaion of machinery shaf and also he axis of roaion. For high speed machinery, such as an auomoile ransmission, hey are he opimal medium for low energy loss and high accuracy. Their funcion is o conver inpu provided y prime mover ino an oupu wih lower speed and corresponding higher orque. Toohed gears are used o ransmi he power wih high velociy raio. During his phase, hey encouner high sress a he poin of conac. A pair of eeh in acion is generally sujeced o wo ypes of cyclic sresses: Bending sresses inducing ending faigue Conac sress causing conac faigue. Boh hese ypes of sresses may no aain heir maximum values a he same poin of conac. [1] However, comined acion of oh of hem is he reason of failure of gear ooh leading o fracure a he roo of a ooh under ending faigue and surface failure, due o conac faigue. The surface failures occurring mainly due o conac faigue are piing and scoring. I is a phenomenon in which small paricles are removed from he surface of he ooh due o he high conac sresses ha are presen eween maing eeh. [9] Piing is acually he faigue failure of he ooh surface. Hardness is he primary propery of he gear ooh ha provides resisance o piing. In oher words, piing is a surface faigue failure due o many repeiions of high conac sress, which occurs on gear ooh surfaces when a pair of eeh is ransmiing power. Gear eeh failure due o conac Faigue is a common phenomenon oserved. Even a sligh reducion in he sress a roo resuls in grea increase in he faigue life of a gear. For many years, gear design has een improved y using improved maerial, hardening surfaces wih hea reamen and carurizaion, and sho penning o improve surface finish ec. This sudy gives an approach o deermine he conac sresses and ending sresses which will help o improvise he performance of he gearing sysem.. LITERATURE REVIEW Invesigaors analyzing he gear ooh for sresses have done several sudies: V. Rajaprahakaran & e al. (013) presened a sudy y adding differen shaped holes o reduce sress concenraion. A finie elemen model of Spur gear wih a segmen of hree eeh is considered for analysis and sress concenraion reducing holes of various sizes are 116

2 inroduced on gear eeh a various locaions. Analysis revealed ha aero-fin shaped hole inroduced along he sress flow direcion yielded eer resuls. A Manoj Hariharan (006) conduced sress analysis on 8 differen gears y deermining he highes poin of conac for all gears. Sress analysis for he load conac poin ravelling along he involue curve is done for gears. The poin of conac where maximum sress occurs is deermined for all eigh es gears and he variaion of his H (Highes poin of Conac) diameer for conac raio greaer han one is sudied. Then he gear raio where i is maximum is aken for applicaion of force for all sudies. From he resuls, he compared he sresses on each gear wih heir respecive highes poin of conacs and seleced he weak gear among hose for sress relief sudies. He inroduced circular holes as sress relieving feaures a differen locaions and also varied he diameers of holes. He concluded wih an opimizaion sudy of drilling wo circular holes, each on wo maing eeh a he same locaion relaive o each ooh, sress can e reduced. Shanmugasundaram Sankar e al., (010) did a sudy using circular roo fille insead of he sandard rochoidal roo fille. The resul reveals ha he circular roo fille design is paricularly suiale for lesser numer of eeh in pinion and where as he rochoidal roo fille gear is more op for higher numer of eeh. Ashwini Joshi and Vijay Kumar Karma (010) did a work which deals wih he effec on gear srengh wih variaion of roo fille design using FEA. Circular roo fille design is considered for analysis. The loading is done a he highes poin of single ooh conac (HPSTC). Vishwas S. Jadhav(007) discusses an experimenal seup which will direcly give sresses a varying load and speed condiions hrough a caliraed elecronic srain gauge indicaor, hey generaed a finie elemen model of spur gear and performed sress analysis while considering addiion of no. of holes in he gear lank. S. Tiwari (01) & e al. uses a 3D model of gear and finie elemen analysis o conduc RBS and SCS calculaion for maing involue spur gears. A pair of involue spur gear wihou ooh modificaion and ransmission error is define in a CAD sysem (CATIA V5 and AUTODESK INVENTOR ec.) and FEA is done y using finie elemen sofware ANSYS. Oained FEA resuls is comparale wih heoreical and AGMA sandard. V. Rajaprahakaran & e al. presened a sudy y adding differen shaped holes o reduce sress concenraion. A finie elemen model of Spur gear wih a segmen of hree eeh is considered for analysis and sress concenraion reducing holes of various sizes are inroduced on gear eeh a various locaions. Analysis revealed ha aero-fin shaped hole inroduced along he sress flow direcion yielded eer resuls. M. Raja & e al. (014) work made an aemp o summarize aou conac sresses developed in a maing spur gear which has involue eeh. A pair of spur gears are aken from a lahe gear ox and proceeded forward o calculae conac sresses on heir eeh. Conac failure in gears is currenly prediced y comparing he calculaed Herz conac sress o experimenally deermined allowale values for he given maerial. The mehod of calculaing gear conac sress y Herzian equaion originally derived for conac eween wo cylinders. Analyically hese conac sresses are calculaed for differen module, and hese resuls are compared wih he resuls oained in modeling analysis in ANSYS. Ali Raad Hassan (009) did a research sudy in which Conac sress analysis eween wo spur gear eeh was considered in differen conac posiions, represening a pair of maing gears during roaion. A programme has een developed o plo a pair of eeh in conac. Each case was represened a sequence posiion of conac eween hese wo eeh. The programme gives graphic resuls for he profiles of hese eeh in each posiion and locaion of conac during roaion. Finie elemen models were made for hese cases and sress analysis was done. The resuls were presened and finie elemen analysis resuls were compared wih heoreical calculaions, wherever availale. The idea of using holes o reduce sresses is no a new one. In 1990, Dippery (Ali Raad Hassan, 009) experimened wih he use of supplemenary holes in a srucure as a mehod of reducing he sress concenraion ha was already presen. His resul showed ha sress concenraion reducions are possile in a generic shape using holes as sress relief. The researchers ill now used circular and ellipical holes as sress relieving feaures wih differen sizes and a various posiions which showed evidence ha sress can e reduced inerruping he sress flow pah from conac poin o fille. 3. STRESS ANALYSIS OF SPUR GEAR 3.1 Analyical Mehod of Sress Analysis Wilfred Lewis in 1893 provides a formula for esimaing he sresses in a ooh. He modeled a gear ooh aking he full load a is ip as simple canilever eam. If we susiue a gear ooh for he recangular eam, we can find he criical poin in he roo fille of he gear y inscriing a paraola. In he Lewis Analysis some assumpions are o e considered which are as follows: The Gear ooh ac as a canilever eam. The Tangenial componen causes he ending momen aou he ase of he ooh. The effec of Radial componens is negleced. The angenial componen is uniformly disriued over he face widh of ooh. The effec of sress concenraion is negleced. 117

3 I is assumed ha a any ime only one ooh will e in conac and akes he oal load. The weakes secion of he gear ooh is a he secion BC, where he paraola is angen o he ooh profile. A he secion BC he momen will e, In his sudy Involue spur gear from he lahe machine gear ox is considered which has following dimensions and maerial properies, Tale Dimensions of he Spur gear where, M P h P m.. Y Dimension Uni Values No. of eeh - 54 PCD Mm 108 The ending sresses are given y, Pressure Angle Deg 0 where, Where, I M. y I. h 3 1 M = Momen a BC m = module of gear Addendum radius Dedendum radius Mm 56 Mm 51.5 Module Mm Face Widh Mm 1 Tale 3 Maerial Properies P = Tangenial Load = Face widh h = deph of ooh Maerial Propery Densiy Uni Grey Cas Iron Kg/m3 700 I = momen of Ineria Young s modulus Pa 1.1E+11 Lewis has defined facor Y, which is also known as Lewis form facor, Tale 1 Values for Lewis form facor for 0o full deph involue sysem Poisson s Raio Bulk Modulus Shear Modulus Pa 8.33E+10 Pa 4.9E+10 Numer of Teeh Lewis Form Facor Y The Lahe machine gear ox is powered y a. Kw moor which provides a Torque of N.m. So, P Torque N Radius M N / m 3.14 y Rack I Kg / m 118

4 Mpa Finie Elemen Mehod for Sress Analysis (ANSYS 14.5) To esimae he sresses he Involue Spur gear ooh is modeled in CreO.0 modeling sofware. The model is hen impored o he ANSYS 14.5 Mechanical modeler for sress analysis under saic loading, he spur gear model is meshed wih Terahedron Elemens wih differen mesh sizes a differen porion for more precise & accurae resuls. The fixed fixed suppor a he ase and wo fricionless suppors a wo slan faces of he geomery wih force acing on he ooh of pinion which acs as canilever. The oundary condiions and force applicaion is also shown in he elow. Figure 3 Force Figure 4 Equivalen sresses of Spur Gear Figure 1 3D Model & Meshed Model of Spur Gear Figure Fixed & Fricionless Suppors 4. Resuls & Discussions The sress reliving feaures are added a differen five locaions across he eeh geomery wih varying sizes. The five locaions are seleced y considering he ooh as a canilever so hree locaions are on he fixed suppor of he canilever whereas wo locaions are across he hanging par of he canilever. The resuls of he same are aulaed elow in Tale No 4. Tale 4 Resuls of sress relieving feaures of differen Sizes a differen Locaions Equivalen (vonmises) Deformaions Toal Locaions Diameers (x,y) (mm) sresses (mm) (mpa) L ( 50.74, 4 ) L (50.74,.43) L (50.74,0.86) L (54,.43) L5 ( 5.5,.43)

5 Figure 5 Equivalen sresses of Spur gear wih sress relieving feaure a locaion 5. Conclusion This sudy mainly focuses on he concenraion of sresses in a gear ooh. The sresses are calculaed analyically using Lewis Formulae as well as using Finie elemen mehod. The resuls from oh he mehods have a sligh percenage of difference, so we can consider FEM resuls for furher sudy wih ease. The effec of sress reliving feaures on he sresses is deermined using finie elemen analysis; five locaions are seleced across he ooh geomery which is analyzed for wo differen sizes of he sress relieving feaure. The es locaion of sress reliving feaure and es size is find ou afer comparing sress analysis a all he pre-seleced locaions and sizes. Acknowledgemen We would like o hank our menor Dr. Sudhir Deshmukh for heir valuale co-operaion & suppor. My colleague Er. farazuddin for his humle correspondence and help during our research paper, all faculy memers of Mechanical Engineering Deparmen and especially he mos, our families for heir forever suppor. [3] Ashwini Joshi and Vijay Kumar Karma (010), Effec on Srengh of Involue Spur Gear y Changing he Fille Radius Using FEA, Inernaional Journal of Scienific & Engineering Research, Vol., No. 9. [4] Hariharan_ME_Thesis (006), Spur Gear Tooh Sress Analysis and Sress Reducion Using Sress Reducing Geomerical Feaures, Thapar Insiue of Engineering and Tech- nology, 006. dspace.hapar.edu:8080/dspace/isream/ /.../ pdf [5] M. Raja, P. Phani, "Conac pressure analysis of spur gear using FEA", Inernaional Journal of Advanced Engineering Applicaions, Vol.7, Iss.3, pp.7-41 (014). [6] S. Shinde, A. Nikam Saic Analysis of Spur Gear Using Finie Elemen Analysis, IOSR Journal of Mechanical and Civil Engineering, PP: 6-31 [7] S. Tiwari, U. Joshi, Sress Analysis of Maing Involue Spur Gear Teeh, Inernaional Journal of Engineering Research & Technology (IJERT) Vol. 1 Issue 9, Novemer- 01. [8] Shanmugasundaram Sankar,Naaraj (010), Profile Modificaion for Increasing he Tooh Srengh in Spur Gear Using CAD, Scienific Research. [9] Sumi Agrwal, R.L. Hime, Evaluion of Bending Sress a Fille Region of an Asymmeric Gear wih a Hole as a sress relieving feaure using a FEA Sofware ANSYS. Inernaional Journal Of Compuer Applicaion Volume 51-No 8, Aug 01 [10] Sushil Kumar Tiwari, Upendra Kumar Joshi, Sress Analysis of moving involue spur gear eeh ISSN: [11] Vivek Karaveer, T. Mogrekar: Modeling and Finie Elemen Analysis of Spur Gear, Inernaional Journal of Curren Engineering and Technology, Vol3., No.5 (Decemer 013). 6. REFERENCES [1] V. Rajprahakaran, R. Ashokraj, Spur Gear Tooh Sress Analysis And Sress Reducion, IOSR Journal of Mechanical and Civil Engineering, PP 38-48, 013. [] Ali Raad Hassan (009), Conac Sress Analysis of Spur Gear Teeh Pair, World Academy of Science, Engineering and Technology, Vol. 3, pp