Die Surface Design and Analysis for Aerofoil Blade using Bezier Curve and Reverse Engineering Method

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1 IJSRD - Interntionl Journl for Scientific Reserch & Development Vol Issue 4 5 ISSN (online): -6 Die Surfce Design nd Anlysis for Aerofoil Blde using Bezier Curve nd Reverse Engineering Method Mnish S til M Tech Student SVNIT Surt-957 Gujrt Indi Abstrct The objective of this work is to develop CAD system which cn be used by forging designers to design forging dies nd test their processes The shpe of the gs turbine blde is the chllenging tsk for the designer becuse this is the complicted section nd the vribles for designing the blde surfce re so mny So chose the right vribles re necessry nd esy control of the shpe is necessry for the design chnges So here I chose the Bezier curve to design the die surfce This is esy to control the shpe of the curve by chnging the control points Key words: CATIA CAD D Scnner purpose nd get the co-ordinte of the profile from which we cn mde the CAD model nd further nlysis cn be done on tht I INTRODUCTION The design nd mnufcturing of gs turbine blde is complicted process Bsiclly the turbine bldes re to be design using the hot forging process Turbine bldes hve complicted shpe nd forging of them needs close control of the process prmeters The objective during design phse is to determintion of finl die shpe s erly s possible to reduce the led time Forging is one of the most common processes of mnufcturing of the turbine blde for the gs turbine ppliction nd power turbine ppliction tht cn sustin the high stresses in the turbine of ircrft engine Die design usully verified with finite element nlysis A detiled simultion of the vrious components is conducted to determine the both residul stress nd finl distortion of the prts Consequently the ppliction of CAD/CAM in the blde forging is the economicl fesible nd is being prctice to vrious level of sophistiction Jurgen M Anders resented pper on prmetric blde design system Germny () Lejun Sho nd Ho Zhou(996) resents the ppers on Curve Fitting with Bezier Cubic s Nzumbe- Mespe Ntoko nd W G Crtwright (98) resented the design of turbo mchine blde cmber surfce using the Bezier technique W Derksen Tim Roglsky () resented the pper on n optimized erofoil prmeteriztion for design using Bezier curve Fig : Wooden Gs Turbine Blde Model For more ccurcy select the less pitch for scnning The minimum pitch for this mchine is 5mm Fig : Window Of Dr icz Needle Scnner The scnning progress of the component the progress of the scnning is shown in the following fig The output of the D scnner gives the co-ordintes of the component From these co-ordintes it is esy to generte the D CAD model II REVERSE ENGINEERING In reverse engineering you re given model which re engineered by someone This product is working product robbly the product developed successfully From the physicl prt scnning is done using the co-ordinte mesurement mchine From tht we import the output of the scnning mchine in to the modelling softwre like CATIA From the point cloud dt generte the surfce model From the surfce some desired chnges is to be done Now the chnged design is used for the mnufcturing of the new component The ctul physicl prt of the gs turbine blde in D is s follow This is the wooden block which is use for the scnning purpose only Use this profile for the scnning Fig : View of rt fter Completion of Scnning Output of CMM-The output files of the CMM re dxf stl txt pix so chose ny one pproprite file formt for import in the modelling softwre The stl file which is to be imported in the CATIA required the normlised file formt for tht copy nd pste the txt file in notepd nd sve it s sc file which is normlised file formt for importing the dt in the CATIA All rights reserved by wwwijsrdcom 9

2 Die Surfce Design nd Anlysis for Aerofoil Blde using Bezier Curve nd Reverse Engineering Method (IJSRD/Vol /Issue 4/5/5) All rights reserved by wwwijsrdcom III BEZIER CURVE FOR DIE DESIGN Bezier curve is prmetric curve (t) tht is polynomil function of the prmeter t The degree of Bezier depends upon the number of control points used to define the curve The curve is not pssed through the intermedite points but is ttrcted by them Ech points influences the direction of the curve by pulling it towrds itself The generl bezier curve Given n+ control points the bezier degree of n is define s B t n i bi Bi n t () Where Bi n t n n i i t n i t i () Are clled the Bernstein polynomil of degree n The quntities n n i i re clled s binomil coefficient n=degree of Bezier curve t=prmeter chosen for Bezier curve The Bezier curve of third degree in generl represented s B = +++ () =[ ( ) ] (4) And the curve in prmetric form is represented s + Then the reltionship is to be express in mtrix form s For finding out the control points tke inverse of the mtrix So in this type we cn find the control points of the Bezier curve represents ny curve in prmetric form nd by compring the prmetric curve with the Bezier prmetric curve IV FORGING DIE SURFACE DESIGN A Representtion of Aerofoil using Bezier Control oints: From the scn dt of the erofoil shpe here I drw the erofoil shpe for gs turbine blde The whole shpe divides in to two section upper prt nd lower prt The upper prt of the scn blde Fig 4: Top Side of the Scn Blde The third degree nd fourth degree eqution of the top side curve is s follow (4) (4) Bottom prt of the scn blde Fig 5: Bottom Side of the Scn Blde The third degree nd fourth degree eqution of the bottom side curve is s follow (4) (44) For the continuity of the curve t the end points the curve must pss through the end points so tht the first derivtives of the curve should be equte with zero We get = (45) by compring the co-efficient nd substitute in the mtrix The co-ordintes of the control points is s follow The stndrd erofoil of the gs turbine blde Fig 6: Stndrd NACA65 Series Aerofoil B Minimize the Actul Devition from the Stndrd: The devition is the difference between ctul nd stndrd profile co-ordintes The min im of the ny mnufcturing

3 process is to reduce the devition or tolernces by compring the stndrd profile with the ctul profile we cn find out the ctul devition To minimize the devition from the Bezier curve nd gives the ctul profile here I superimpose the control points on ech other so tht it gives the higher degree curve nd less devition Die Surfce Design nd Anlysis for Aerofoil Blde using Bezier Curve nd Reverse Engineering Method (IJSRD/Vol /Issue 4/5/5) Fig : The Devition of the Vrious Superimpose Fig 7: D Bezier Curve nd Its Control oints Fig : Bezier Curve fter Superimposing First Control oint Fig 8: Bezier Curve fter Superimposing First Control oint Fig 4: Bezier Curve fter Superimposing Second Control oint Fig 9: Bezier Curve fter Superimposing Second Control oint Fig 5: Bezier Curve fter Superimposing Third Control oint Fig : Bezier Curve fter Superimposing Third Control oint Fig 6: Bezier Curve fter Superimposing Fourth Control oint Fig : Bezier Curve After Superimposing Fourth Control oint Fig 7: The Devition of the Vrious Superimpose All rights reserved by wwwijsrdcom

4 Die Surfce Design nd Anlysis for Aerofoil Blde using Bezier Curve nd Reverse Engineering Method (IJSRD/Vol /Issue 4/5/5) C Die Design rocedure: The dies re mde of costly tool steel nd re hrden to RC 58-6 hrdness nd it is mnufctured by electricl dischrge mchining (EDM) but the process is very slow nd rther costly The deflection of the bottom die is within the limit The lower tool cn be simply supported bem with uniformly distributed lod The deflection cn be found out from the following reltion (46) where w=lod on bolster plte L=spn between prllel block E=modulus of elsticity (8 5 M for steel bolster) I= moment of inerti Compute the die deflection for the bove pressure The pressure on the die is 45M so the lod in 5KN Hence the deflection of the die is W=45KN L=6mm b=6mm E=modulus of elsticity =G Deflection d=74677mm This is the permissible vlue of deflection of the die t the centre of the die which is mximum deflection without filure of the die Computing die thickness nd mrgins The tensile stress on die depends upon the verticl force it s lso depends upon the thickness of the die The thickness of the die cn be clculted by using the following formul [ [ ] [ ] ] (47) T=thickness of the diev=verticl force (N) Ft=permissible tensile stress B=width of the slot A=length of the slot d=dimeter of screw Mrgin usully rnges from one to two times die thickness to By clcultion we get the thickness of the die s T=8mm (by including the tolernces of mm) Mrgin M=8mm The top die for the erofoil gs turbine blde is s follow in CATIA Fig 9: Bottom Die Model of Die in CATIA D Anlysis of Die: Fig : Totl Deformtions of Top Die Fig : Von Mises Stresses in Top Die Fig : Totl Deformtions of Bottom Die Fig 8: Top Die Model of Die in CATIA And the bottom die for the erofoil gs turbine blde is s follow Fig : Von Mises Stresses of Bottom Die V RESULTS AND DISCUSSION The NACA stndrd erofoil nd scn erofoil blde for gs turbine All rights reserved by wwwijsrdcom

5 Die Surfce Design nd Anlysis for Aerofoil Blde using Bezier Curve nd Reverse Engineering Method (IJSRD/Vol /Issue 4/5/5) Fig 4: Comprison between Stndrd nd Actul rofile The devition of the bove two erofoil curve for the top section is s follow Fig 5: Devition between Stndrd nd Actul rofile for Top Die The devition of the bove two erofoil curve for the bottom section is s follow Fig 6: Devition between Stndrd nd Actul rofile for Bottom Die And the mximum devition of the Bezier curve from the stndrd curve for top curve is 75 per unit width nd for the bottom curve is 497 per unit width Now here I chose the width of the blde s mm so the mximum devition of the turbine blde is mm Mximum devition = 47mm deflections of the lower die is clculted from the formul W=intensity of lod L=length of die E=modulus of elsticity I=moment of inerti By clcultion the deflection of the bottom die is d=74677mm And from the nlysis the deflection is s Top die (mx) Bottom die (mx) Deflection 69664mm 754mm Tble : So the deflection of the die is within the limit the design is sfe for the bove lod condition The von mises stress on the die is s follow Top die Bottom die Von mises stresses 59M 7M Tble : VI CONCLUSIONS The new pproch of design for the forging die surfce using the Bezier curve is presented This wy of design the die surfce for forging of the gs turbine blde is more flexible The designer needs to chnge only the control points of the Bezier curve for the chnge of the curve The prmeteriztion of the curve which got form the reverse engineering of the wooden erofoil is done by selecting pproprite prmeter nd these prmetric eqution is solve by using the mtrix form nd then compre these curve with Bezier stndrd prmetric curve nd solve these eqution for the control points of the Bezier curve To minimiztion of the devition the superimpose of the Bezier control points is lso presented by compring vrious superimposing points I found tht single point superimpose is effective nd good result method to minimize the ctul devition The third point from the strting is superimpose gives the less devition s compre with other points So use those superimposing for the design of the erofoil nd mke the model nd further nlysis is to be done on tht model which gives the stresses re within the limit hence the design is sfe REFERENCES [] B Lu H Ou CG Armstrong A Rennie(9) D die shpe optimistion for net-shpe forging of erofoil bldes Mterils nd Design (9) 49 5 Queen s University Belfst Belfst BT9 5AH UK [] B Lu HOu () An efficient pproch for trimming simultion of D forged components Interntionl JournlofMechniclSciences55() 4 Shnghi Jio Tong University Shnghi Chin [] Christin Vessz Christophe Tournier Ce cile Mu nch Frnc ois Avelln() Design optimiztion of D blde by mens of milling tool pth CIR Journl of Mnufcturing Science nd Technology 6 () E cole polytechnique federle de Lusnne Switzerlnd [4] F Jvidrd R Rhmti (9)An integrted reengineering pln for the mnufcturing of erospce component Mterils nd Design (9) 54 5 University of Aeronuticl Science nd Technology Tehrn Irn [5] H Ou R Blendr(998) Die-elsticity for precision forging of erofoil sections using finite element simultion Journl of Mterils rocessing Technology 76 (998) 566University of Strthclyde Glsgow UK [6] H Ou J Ln CG Armstrong MA rice (4) An FE simultion nd optimistion pproch for the forging of ero engine components Journl of Mterils rocessing Technology 5 (4) 8 6 Queen s University Belfst UK [7] Hkim S Sultn Aljibori (9) Finite Element Anlysis of Sheet Metl Forming rocess Europen Journl of Scientific Reserch ISSN 45-6 Vol No (9) pp57-69 Mechnicl Engineering Deprtment Fculty of Engineering University Mly 56 Kul Lumpur Mlysi [8] Jn sinczk Anet lukszek-solek Sylwi Bednrek wel Chyl() The forging process of ircrft All rights reserved by wwwijsrdcom

6 engine turbine bldesmetllurgy nd foundry engineering-vol 6 No AGH university of science nd technology Krkow olnd [9] K H Lee H Woo nd T Suk () Dt reduction methods for reverse engineering Interntionl Journl of Advnced Mnufcturing Technology 7() pp [] Lejun Sho nd Ho Zhou(996) Curve Fitting with Bezier Cubics Grphicl models nd imge processing Vol 58 No My pp 996 Article no 9 Nnyng Technology University Nnyng Avenue Singpore 64 Singpore [] Ling-Chi Chen Grier CI Lin()Reverse engineering in the design of turbine bldes- cse study in pplying the MAMDRobotics nd Computer Integrted Mnufcturing () 667 Centre for Advnced Mnufcturing Reserch School of Engineering University of South Austrli Austrli [] Lizheng Lu(9) Approximting tensor product Bezier surfces with tngent plne continuity Journl of Computtionl nd Applied Mthemtics (9) 44 Zhejing Gongs hng University Chin [] M Lounsbery S Mnn nd T DeRose (99) rmetric surfce interpoltion IEEE Computer Grphics nd Applictions Die Surfce Design nd Anlysis for Aerofoil Blde using Bezier Curve nd Reverse Engineering Method (IJSRD/Vol /Issue 4/5/5) All rights reserved by wwwijsrdcom 4