COMPUTER MODELLING AND FINITE ELEMENT ANALYSIS OF TUBE FORMING OPERATIONS D.S.Shamasunda, Manu Mathai, Sachin B M INTRODUCTION: Tubula sections can be conveted into a vaiety of poducts. One o moe foming pocesses can be used, including Tube Hydofoming, Tube pilgeing, Tube bending etc. Finite Element Method (FEM) has been used fo optimization of the above mentioned foming pocesses with a view to maximize defomation in ode to aid in the fomation of complex pofiles. Designing with FEM can minimize costly expeimentation and ty-outs and educe tool and mateial wastage theeby enabling to get the pocess ight at the fist ty-out. Moeove the limits of fomability and vaious pocess Kinematic elationships can be easily established which can lead to bette poductivity. MECHANICS OF TUBE FORMING: In the Tube-foming pocess, the tube is eithe closed at both ends by igid plugs, o povided with floating pistons, which allow fee axial contactions. The tube is assumed so lage that plane tansvese sections emain plane duing the expansion. This means that the longitudinal stain ε z is independent of the adius to the element. The intenal and extenal adii of the tube is a and b and the tube is subjected to an intenal pessue p and a Longitudinal foce P. The stesses and stains sufficiently fa fom the ends do not vay along the length of the tube and the equations of equilibium is : σ = σ θ σ The z axis of the cylindical co-odinates(,θ,z) is taken along the axis of the tube. When the tube is entiely elastic, the longitudinal stesses may be witten fom Hooke s law as : σz = Eεz + ν( σθ + σ) Denoting the adial displacement by u, the adial stain ε cicumfeential stain ε θ may be witten as : and the
] ) [( E u ] ) [( E u z z νσ ν σ +ν + = νε = ε νσ ν σ +ν + = νε = ε θ θ θ Since ε z is independent of, the following Compatibility Equation can be obtained: 0 ) ( = +σ σ θ By analysis using Lame s Solution the stesses theefoe become + = σ = σ θ a b b p a b b p If the esultant longitudinal load is denoted by P, then the axial stess is : ) a (b P z π = σ FEM can be used fo accuate estimation of the axial, adial and cicumfeential stesses and stains to accuately pedict failue and distotion in the fomed tube component at any location.
TUBE HYDROFORMING: In the tube hydofoming pocess the tubula blank is pefomed by bending and inseted into an axially o adially split die. Then the die is closed cushing the tube and the tube is sealed at each end. Finally, Hydaulic liquid fills the tube and hydaulic pessue is applied inside the tube whilst simultaneous axial loading is applied at the ends of the tube pushing it into the die. The tube wall is thus pessed and the intenal contou of the die and pat is fomed. Thus the intenal pessue and the axial loading ae the two key paametes of the pocess. These two paametes have to be optimised fo the successful opeation of the pocess. Thee ae fou types of failue modes of tube hydo fomed components: a) Buckling-This is caused due to excessive axial compessive defomation. b) Winkling - This is caused due to excessive axial loading o insufficient intenal pessue. c) Busting -This is caused due to the thickness of the tube blank being smalle than needed to sustain the hoop stesses o due to the axial loading being insufficient. Thus it is obseved that impope atio of intenal pessue and axial loading cause the failue of the tube blank by Buckling, Winkling o Busting. Thus thee is an ugent need to optimize the pocess though the use of the Finite Element Method (FEM). FEM can be used to optimize the pessue-time cycle needed fo maximum and optimum defomation behaviou. The maximum defomation behaviou is elated to the mateial popeties like stain ate, tempeatue and gain size. The mateial has to be woked at ideal limits of stain ate, tempeatue etc to achieve maximum defomation without factue. This is achieved though FEM simulations by vaying the pessue -loading cuve with time so that the mateial opeates at its ideal possible limit. This obviates the need to conduct costly and tedious expeimentation needed to optimize the pessue loading cycles. The axial loading impated to the punch can also be optimised though the use of FEM and coective measues can be ecommended by obseving the defects and failue mechanisms. FEM can also be used to establish the pope Kinematic elationships fo the pocesses and pediction of limits of Fomability and loads needed fo optimizing the pocesses. 3
Fig (a)&(b) shows the hydo foming of STAMPACK-FEM based package. tube simulated though Fig(a) :Relative thickness of tube afte Hydofoming. Fig(b): Total displacement of tube afte hydo foming. 4
TUBE PILGERING : Tube educing is the pocess of educing the coss sectional aea by olling the tube ove a tapeed mandel using semicicula dies with tapeing gooves. These dies do not otate, but ock back and foth. The mandel and the tube ae otated between stokes & move fowad at the same time. Expeimental detemination of metal defomations in the tube cold olling pocess in Pilge mills poses a lot of technical poblems. High speed of the olling stand in the ecipocating motion makes immediate switching off in a pecisely selected point of the olling zone impossible. Compact and closed stuctue of the olling mill, in paticula of its woking space, makes impossible to place sensos fo measuing defomations, connecting measuing signals to the amplifying and ecoding equipment and potecting them against impact of high pessue olling emulsion mist. Theefoe,the physical modeling method though FEM is applied in investigations of the defomation aea in the cold tube Pilgeing pocess. Though the use of FEM we can accuately estimate the defomations, stesses and damage at any point of inteest in the defomation zone. TUBE BENDING : Tube bending equies intenal suppot in the inne side of the tube bend. Mandels ae used in bending to pevent collapse of the tubing. The need fo a mandel depends on the tube and bend atios. The tube atio is D/t whee D is the oute diamete and t is the wall thickness. The Bend atio is R/D whee R is the adius of the bend measued to the centeline. The wall thickness of the tubing affects the distibution of tensile and compessive stesses in the bending. A thick wall tube will usually bend moe easily to a smalle adius than a thin wall tube. The fou most common methods of bending tubing ae Compession bending, stetch bending, daw bending and oll bending. The method selected fo a paticula application depends on the equipment available, the numbe of pats equied,the size and wall thickness of the tubing, the wok metal, the bend adius, the numbe of bends in the wokpiece. FEM can be used fo estimating the optimum thickness needed fo easy bending and fo pedicting the distibution of tensile and compessive stesses at any section of the bend. 5
FEM Simulation of TUBE BENDING: In FEM based Tube bending we can detemine Residual Stesses, Radial Stess & Stain distibution. Also we can simulate fo sping back effect of the tube. Half symmety is modeled by declaing the nodes in the symmety plane as non-sepaable fom the symmety plane as shown in the figue. Pocess Paametes Tube tempeatue = 0 DEG C Die speed = adian/sec Fiction facto = 0.0 Bounday conditions Bottom face of tube is fixed. Symmety plane of tube is made non-sepaable with the symmety plane Fig : Tube Bending die aangement & FEM Mesh geneated fo Simulation. 6
Fig (d): Effective Stess distibution in a tube bending opeation. TUBE SPINNING: Tube spinning is a otay point method of extuding metal much like cone spinning. Spinning is one method of educing the wall thickness of tubula shapes and inceasing thei stength, paticulaly fo aicaft and aeospace applications. Poducing specific shapes fom tubing is a majo function of tube spinning. Fo example, one o moe flanges can be spun at selected aeas on a tube, often at a savings in labo and mateial costs when compaed with othe pocesses such as machining. Fig (e) shows the mandel, wokpiece & olle aangement. Fig (f) the spun tube at the end of the spinning pocess. This pocess can be modeled & simulated on FEM tool. 7
Wok piece Mandel Rolle Fig (e): Tube spinning aangement. Fig (f) : End pocess of tube spinning. 8
TUBE FLAIRING : Below fig shows the effective stess distibution duing a tube flaiing opeation analyzed though FEM based simulation. It also demonstates defomation & die etaction. Contous of effective stess duing defomation & afte die etaction (esidual stesses) ae also obtained simulation Fig(g). Thee is sping back effect obseved at the end of pocess Fig(h). Fig(g) : Effective stess distibution in tube flaiing opeation obtained though simulation. Fig (h): Sping effect in tube flaiing opeation. 9
TUBE UPSETTING: Tube upsetting can be simulated on DEFROM A FEM tool to check the die design & based on the esults we can optimize the die design. One such simulation example is given in Fig (i), which shows the fold in the tube at the final stages of tube upsetting. This defect can minimized by optimum die design. Mandel Fold in Tube Die Fig (i) : Tube upsetting simulation esult showing Fold in the tube. 0
TUBE SWAGING : Tube swaging is a pocess fo educing the coss sectional aea o othewise changing the shape of the tubes by epeated adial blows with two o moe dies. The wok piece is elongated as the coss sectional aea is educed. The wok piece is usually ound o squae o othe wise symmetical in coss section can swaged. Fig (j) shows one such set up of tool fo tube swaging in which thee ae fou dies aanged adially. The same tool set up is used in simulation. Anothe fig(k) will show the educed coss section afte swaging pocess. Fig (j): Tube swaging showing tool setup.
Fig (k) : Reduced coss sectional aea afte swaging opeation,simulated in DEFORM package. CONCLUSION : Based on the simulation esults we can conclude that FEM is an impotant design tool which can be used fo pocess optimization and design of tube foming pocesses. Innovative design modifications can be tested on the compute using FEM and the ideal pocess can be developed and got ight at the fist ty-out in the shop floo theeby minimizing costly and tedious expeimentation. REFERENCES:. Metals Handbook, Ninth Edition Vol.4, Foming and Foging. ASM Intenational.. Mechanical Metallugy, G.E.Diete, Mc Gaw Hill, 976. Theoy of Plasticity, J.Chakabaty, Mc.Gaw Hill Intenational Edition.,987. 3. DEFORM 3D USERS MANUALS.
4. S.I. Oh, W. T. Wu, J. P. Tang and A. Vedhanayagam Capabilities And Applications Of FEM Code DEFORM;The Pespective Of The Develope, Jounal of Mateials Pocessing Technology, Elsevie, Vol. 7, pp. 36-38, 99. 5. J.Waltes Application Of The Finite Element Method In Foging; An Industy Pespective, Jounal of Mateials Pocessing Technology, Elsevie, Vol. 7, pp. 43-5, 99. 6. J. P. Tang, W. T.Wu and J. Waltes Recent Development And Applications Of Finite Element Method In Metal foming, Jounal of Mateials Pocessing Technology, Elsevie, Vol. 46, pp. 0-, 994. 7. M.G. Cockoft and D. J. Latham Ductility And The Wokability Of Metals, Jounal of the Institute of Metals, Vol. 96, p33-39, 968. 8. Y. Kim, M.Yamanaka and T.Altan K. Lange, A.Hettig and M.Knoe Inceasing Tool Life in Cold Foming though Advanced Design and Tool Manufactuing Techniques, Jounal of Mateials Pocessing Technology, Vol. 35, pp. 495-53. 9. W. T. Wu, G. Li,A. Avind and J. P.Tang Development Of A Thee Dimensional Finite Element Method Based Simulation Tool Fo The Metal Foming Industy, pesented at the Thid Biennial Joint Confeence on Engineeing Systems Design and Analysis, July -4, 996, Montpellie, Fance, confeence poceedings. 0. J. Waltes, S.Kutz, J. Tang and W. T. Wu The State Of The At In Cold Foming Simulation, Jounal of Mateials Pocessing Technology, Elsevie, Vol.7, pp. 64-70, 997.. J. Waltes Application Of The Finite Element Method In Foging; An Industy Pespective, Jounal of Mateials Pocessing Technology, Elsevie, Vol. 7, pp. 43-5, 99.. J. Domblesky and J. Waltes Pocess Modeling Fo Foging Die Stess Analysis, wokshop notebook, 996 998. 3. K. Aimoto, G. Li, A. Avind, and W. The Modeling of Heat Teating Pocess, being submitted, Scientific Foming Technologies Copoation, 998. 3