Optimum Design of Pipe Bending Based on High- Frequency Induction Heating Using Dynamic Reverse Moment

Transcription

1 Optiu Design of Pipe Bending Based on High- Fequency Induction Heating Using Dynaic Revese Moent Pipe bending by high-fequency local induction heating is an advanced technique used to bend pipes having a sall bending adius and a lage diaete. Although pipe bending is a widely used engineeing pocess, the optiu pocess paaetes ae decided on the basis of a tial and eo ethod by highly expeienced field enginees. Hence, it is necessay to develop an integated ethodology fo the optiu design of the pipe bending pocess. Duing hot-pipe bending using induction heating, the thickness of the oute wall of the pipe deceases because of tensile stess, but the thickness is not allowed to decease by oe than 12.5%. The use of the DOE ethod and a dynaic evese oent is poposed fo aintaining the thickness eduction atio to within 12.5%, when D/t is high. The esults of the poposed appoach ae found to be in good ageeent with those of FEA. Manuscipt eceived: Febuay 9, 2011 / Accepted: June 7, 2011 NOMENCLATURE D = oute diaete of pipe () M b = bending oent (kn ) M c = evese oent (kn ) R = bending adius () = pipe adius () = aveage adius of pipe () t = pipe thickness () t 0 = initial thickness of pipe () β = angle of neutal axis ( o ) R = distance between neutal axis and x-axis ρ = adius of cuvatue 1. Intoduction Pipe bending pocess by high-fequency local induction heating is coonly used fo pipes having a sall bending adius and a lage diaete, without the need fo a old. This technique has been used widely in powe plant and shipbuilding plant. 1-3 The afoeentioned technique offes seveal advantages ove conventional pocesses that involve olding and welding, such as low cost, high poductivity, and affods poducts with good ateial popeties. 1,4 Bending pocess ae studied fo vaious ateials. 5 Howeve, pipe bending is a coplex pocess since it involves theal bending and high-fequency local induction heating. Duing pipe bending, the oute wall of the pipe is thinned owing to tensile stess, while the inne well is thickened because of copessive stess. In engineeing design, the thinning of the pipe wall is not allowed to exceed 12.5% because the poducts of pipe bending ae geneally used to tanspot fluids with high tepeatue and pessue, and poducts in which the wall thickness deceases beyond the afoeentioned liit would be unsuitable fo this pupose. 6 W. Zutang et al. 6 deived a foula fo a dynaic evese oent to be used when bending pipes with a sall bending adius. Z. Hu et al. 1,3 poposed a ethod fo deteining the wall-thickness eduction on the basis of the bending angle, bending foce, evese oent, and sping-back angle, by using copute siulations. Ki et al. 7 investigated the effect of the evese oent and tepeatue gadient on wall-thickness eduction, and applied the evese oent to an actual pipe-bending pocess. The atio of the bending adius of a pipe (R) to its oute diaete (D) is given by DR. In the case of a pipe with a sall

2 ' ' ' ' 1052 / DECEMBER 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 dl dl' sinβ Fig. 1 Model of the hot pipe bending pocess using induction heating ρ(ϕ) dϕ dϕ' t θ β O R R y Fig. 2 Position of neutal axis with espect to evese oent bending adius which is less than 1.5 DR and a elatively lage oute-diaete-to-thickness atio (D/t), the citeion that the wallthickness eduction should not exceed 12.5% is not satisfied, and ovality occus at the bending aea. In this study, the effect of the design factos used in the pipe bending pocess on an objective function ae analyzed by using the DOE (design of expeient) ethod. An optiu pipe-bending pocess with iniu wall-thickness eduction is designed on the basis of the analysis esults. Then, a evese oent is applied to the aea in which the wall-thickness eduction is oe than 12.5%. 2. Theoetical Analysis of Pipe Bending Pipe bending based on high-fequency local induction heating involves (1) high-fequency local induction heating, (2) feeding of the pipe, and (3) clap pat. The odel of the afoeentioned hotpipe bending pocess is shown in Fig. 1. One end of the pipe is fixed with the help of a bending a pivotable about otation axis, and a bending foce is applied to the othe end by the tanspotation equipent. Upon induction heating, a bending oent is geneated in the heating aea, and the pipe is bent. Then, the pipe is cooled by spay-cooling with cooling wate. 2.1 Thickness Reduction Ratio In the theoetical analysis of the hot-pipe bending pocess, it is assued that the pipe ateial is igid plastic and incopessible. The equation fo the thickness eduction atio when the aveage adius of the pipe is assued to eain unchanged afte bending is 6 t 1 cosβ = t R/ + cosβ 0 (1) Fig. 3 Sping-back defoation 2.2 Revese Moent 1 The position of the neutal axis elative to the evese oent is shown in Fig. 2. The neutal axis is shifted outside the bending aea by the evese oent, and the bending aea unde the tensile stess is deceased. This, in tun, bings about a decease in the thickness eduction atio. The evese oent, M c, satisfying the design conditions fo pipe bending is given by Eq. (2). 2 ( π 2 β)cosβ + 2sinβ R M = 2 σ t ( 2 ) c s 0 π β + 2( R / + cos β ) ( π 2 β) + sin2β 2sinβ 4( R/ + cos β ) 2.3 Sping-back In the pipe-bending pocess, which has elasto-plastic behavio, sping-back defoation occus afte unloading the bent pipe. Defoation caused by sping-back is shown in Fig. 3, and the equation fo pedicting the sping-back angle is given by Eq. (3). 3 (2) d( ϕ') = dϕ dϕ' (3) Hee dφ and dφ' ae the bend angle of the infinitesial segental pipe befoe and afte sping-back, espectively. The stain of the bent outside fo sping-back is given by Eqs. (4) and (5). 3 dl dl [ ρϕ ( ) + (1 sin β)] dϕ ( R + ) dϕ ε = = z dl ( R + ) dϕ (4) σ k z ε = = (1 sin β) (5) z E E 3. Finite Eleent Analysis of Hot-Pipe Bending The effect of the design factos used in hot-pipe bending on the thickness eduction atio is investigated by the DOE ethod. The steps equied fo a obust design of pipe-bending pocess ae decided on the basis of the FEM (finite eleent ethod) and ae shown in Fig. 4. 8

3 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 DECEMBER 2011 / 1053 CAD Model Initial design Technological paaete Contol Facto Othogonal Aay FEM Model Siulation Siulation Result s tic is te c a a h c e c n a f o e P Othogonal Aay Calculate SN Ration, Sensitivity Inne Table Statistical Analysis Robust design (a) Tensile specien Contol Facto 1. Heating tepeatue 2. Tepeatue gadient 3. Revese oent 4. Feeding velocity 5. Heating width Pefoance chaacteistics Pipe thickness eduction atio Fig. 4 Steps in obust design of pipe-bending pocess, as decided by FEM 3.1 Modeling and Bounday Condition Fo obtaining data petaining to the popeties of the pipe ateial (A 106 G. B), a high-tepeatue tensile test is pefoed. Fou test tepeatues-900 C, 950 C, 1000 C, 1050 C-ae eployed, and at each tepeatue, five stain ates ae used: s -1, 0.02s -1, 0.034s -1, 0.048s -1, and s -1. The tensile specien, tensile teste (MTS) and the stess-stain elationship at each tepeatue fo the aboveentioned stain ates ae shown in Fig. 5. Pipe odels used in the actual field ae shown in Fig. 6. The atios of the adius of cuvatue to the oute diaete (ρ/d) ae the sae fo all the pipe odels; howeve, the outediaete-to-thickness atio (D/t) is diffeent in each case. The coecial code Defo 3D is used fo the elasto-plastic FEM analysis. The pipe odel is designed with 1/2 syety because the pipe ust be ade syetic in the cicufeential diection fo educing the analysis tie. To ensue high accuacy of the analysis, the gids in the aea subjected to local induction heating ae ade elatively dense, and the esh nube is set to 10,000 by taking into account the defoation of the pipe and copute analysis tie. The FEM odeling of pipe bending is shown in Fig. 7; it is assued that the pipe ateial is elasto-plastic and that the dies ae igid. The shea fiction between the punch and the pipe is assued to be of non-sepaate type, and thee is no fiction in the othe pats of the odel (between the guide ing and the pipe, and between the pivot and the pipe), as shown in Fig. 8. To apply the effect of local induction heating, the tepeatue at each node in the pipe odel is changed at specific tie intevals. Because of the tepeatue vaiation in the odel, thee zones can be identified: a peheating zone esulting fo heat conduction, a defoation zone caused by local induction heating, and a cooling zone (Fig. 9). To investigate the dependence of the thickness eduction atio on D/t, we pefo finite eleent analysis (FEA) fo thee cases; the pocess vaiables used in all the cases ae the sae (Table 1). The change in the thickness eduction atio with the bending angle is shown in Fig. 10. In case 1, the diffeence between the axiu (A) and the iniu (B) thickness eduction atios is 3.2%; this diffeence is geate than that in case 2 and case 3 (1.9% and 1.4%, espectively). When the thickness eduction atio changes with the (b) MTS tensile teste (c) Stess-stain cuve Fig. 5 Stess-stain elationship fo diffeent stain ates D:168.3 A Detail A Fig. 6 Pipe odeling on the basis of D/t t:7.1 Case 1. D/t : 23.7 Case 2. D/t : 18.1 Case 3. D/t : 15.3 t:11.0 t:9.3 bending angle because of the elatively lage diffeence between the A and B values, it is difficult to ensue that the wall-thickness eduction is less than 12.5%, and hence, a evese oent ust be applied.

4 1054 / DECEMBER 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 Pipe (A106B) Pivot (Rigid) Table 2 Feeding oent and liit evese oent decided by FEM D/t Moent (t:7.1) (t:9.3) (t:11.0) Feeding oent 23.22KN 31.30KN 36.93KN Liit evese oent 13.93KN 18.78KN 22.16KN Liit evese oent: 60% of the feeding oent Guide Ring (Rigid) Punch Fig. 7 Modeling fo pipe bending (Rigid) (a) Angle befoe sping-back (b) Angle afte sping-back Fig. 11 FEA esults of sping-back angle Fig. 8 Bounday conditions fo pipe bending pocess Pipe outsied wall t V=0.5~1.5/s Pipe insied wall peheating zone defoation zone C 1050 B 950 A 850 Cooling zone Pipe outsied wall A B C Pipe insied wall Fig. 9 Vaiation in tepeatue with heating tie at each node Table 1 Pocess vaiables fo FEA R.M (KN ) T.G H.T (/in) () Case 1~ R.M: Revese oent(kn ) T.G: Tepeatue gadient H.T: Heating tepeatue : Feeding velocity(/in) : Heating width() Fig. 10 Vaiation of thickness eduction with D/t when the oute diaete is In case 1 (axiu value of D/t), whee the diffeence between the A and B values is the lagest aong that in all thee cases, the liit evese oent is elatively sall; hence, it is difficult to aintain the equied thickness eduction atio constant when the bending angle changes. In case 3, a evese oent geate than that in cases 1 and 2 can be applied, and theefoe, the thickness eduction atio can be aintained constant. FEA is pefoed fo case 1 (D=168.3, t=7.11), whee the sall liit evese oent and the lage diffeence between A and B values akes it difficult to obtain a constant thickness eduction atio. 3.2 Analysis of Sping-back Fo pedicting a sping-back angle, FEA is pefoed using the conditions in Table 1. As shown in Fig. 11, the bending angles befoe and afte sping-back ae 90 and 89.1, espectively. By using FEA and Eq. (3), the sping-back angle is obtained as 0.9. Theefoe, it is necessay that the bending angle is odified by consideing sping-back because the acceptable toleance of the pipe bending-angle is 90 ± Robust Design Design Vaiables and Contol Facto Levels The odel used fo the obust design of hot-pipe bending is shown in Fig. 12. The objective function fo the pocess design is that the thickness eduction atio ust not exceed 12.5%. The contol factos that affect the thickness eduction atio ae heating tepeatue, tepeatue gadient, evese oent, feeding velocity and heating width. The agnitude of the evese oent is chosen on the basis of the theoetical analysis (Eq. (2)), and the initial values of the design factos ae deteined on the basis of expeiental knowledge of the field (Table 3) Othogonal Aay The level of each contol facto is set at 4 on the basis of the values listed in Table 2 (Table 4). An L16 othogonal aay that accoodates five design factos at fou levels is used, and it is assued that thee is no inteaction between the factos. The conditions and aangeent fo each expeient ae shown in Table 5.

5 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 DECEMBER 2011 / 1055 Taguchi ethod fo 1.5D pipe bending pocess Feeding Velocity(/in) Heating Tepeatue( ) Tepeatue Gadient( ) Revese Moent(KN ) Outside Inside Design Intention : The thinning of pipe wall is not allowed to exceed 12.5% Pefoance chaacteistic : Pipe thickness eduction atio, Salle is bette Design Taget : Signal-to-Noise Ratio, Salle is bette Contol Factos : Revese Moent Heating Width () Tepeatue Gadient Heating Tepeatue Feeding Velocity Heating Width Fig. 12 Model fo obust design of hot-pipe bending Table 3 Initial design fo 1.5DR pipe bending Design paaete R.M (KN ) T.G H.T (/in) () Value t0 t Table 6 SNR fo obust design NO. T.R(%) SNR NO. T.R(%) SNR T.R: Thickness eduction atio(%) SNR: Signal-to-noise atio Table 7 SNR esponse Level R.M T.G H.T δ Rank Main Effects Plot (data eans) fo SN atios R.M T.G H.T Table 4 Contol facto levels Facto Level R.M (KN ) T.G H.T (/in) () s -25 io t a -26 N S f o n a -23 e M Table 5 Expeient aangeent (inne table L 16 (4 5 )) Facto NO. R.M (KN ) T.G H.T (/in) () Pocess Design Because a sall thickness eduction atio is pefeed fo ou objective function, the salle-the-bette-chaacteistic given by Eq. (6) 9 is used: SNR = Σ y n (6) 2 10log ( / ) 10 i Whee n is the nube of the expeients, and y is the value of the chaacteistic. The signal-to-noise atio (SNR), which is calculated by using Eq. (6), inceases with a decease in the Signal-to-noise: Salle is bette Fig. 13 Main effects plot fo SNR thickness eduction atio, as is evident fo the data shown in Table 6. The SNR esponse and ain effect plot fo the SNR ae shown in Table 7 and Fig. 13, espectively. The contol facto that has the stongest effect on the thickness eduction atio is the evese oent (δ=3.02, Rank 1), and the effect of the othe factos is in the following ode: heating width (δ=2.79, Rank 2) > heating tepeatue (δ=1.32, Rank 3) > tepeatue gadient (δ=1.27, Rank 4) > feeding velocity (δ=0.07, Rank 5). Because the neutal axis is focibly shifted outside the pipe, the thickness eduction atio is salle when the evese oent is stonge. Howeve, when the evese oent is stonge than the feeding oent, buckling occus at the inne wall of the pipe, o pipe bending becoes ipossible. Theefoe, the evese oent is liited to about 60% of the feeding oent in the field. Because a lage heating width ay esult in necking, buckling and poo out-of oundness, the heating width is geneally liited to a value that is twice the pipe thickness. 1 A tepeatue gadient is ceated because the egion unde copessive stess has elatively high tepeatue and that unde tensile stess has a low tepeatue; consequently, the defoation esistance in the tensile-stess egion is highe than that in the copessive-stess egion. Theefoe, defoation of the 12 14

6 1056 / DECEMBER 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 Fig. 14 Thickness eduction atio fo diffeent bending angles when D/t is high Fig. 16 Vaiation of thickness eduction fo vaious evese oents Fig. 17 Revese oent diaga obtained fo Fig. 14 Fig. 15 Pipe shape siulated on the basis of the esults of design expeient oute diaete of the pipe is suppessed, and the thickness eduction atio is deceased. The optial values of the evese oent (11.36kN ), tepeatue gadient (80 C), heating tepeatue (980 C), feeding velocity (40/in) and heating width (14) ae obtained on the basis of the ain effects plot fo the SNR. FEA is pefoed fo the optial pocess; the esults of thickness eduction atio and pipe shape ae shown in Fig. 14 and Fig. 15, espectively. The aveage thickness eduction atio deteined by FEA, 11.65%, is less than the eduction atios fo the 16 cases in the othogonal aay. Howeve, the eduction atio in the specific te (about 18 ) in Fig. 14 is 13.1% which is geate than the liit thickness eduction atio, 12.5%; this tend is ponounced at a high D/t. Ovality occus at bending angles of because of the eduction in the inne diaete of the pipe. 3.4 Applying a Dynaic Revese Moent When the thickness eduction atio is less than 12.5%, a pipe with a high D/t is not obtained even afte the pocess design is optiized by the DOE ethod, and pipe ovality occus. A evese oent lage than 11.36kN is equied when the bending angle is in the ange because that the citeion of the liit evese oent is not satisfied. A evese oent salle than 11.36kN is equied fo the bending angle ange Fig. 18 FEA esults obtained when a dynaic evese oent is applied because a lage evese oent ay esult in ovality. The change in thickness eduction with the evese oent is shown in Fig. 16. Fig. 17 shows the dependence of the evese oent on the bending angle fo the case whee the evese oent is less than the liit thickness eduction atio of 12.5%; the data fo Fig. 16 have been used fo this plot. The FEA esults obtained when applying the dynaic evese oents and the pipe shape ae shown in Fig. 18 and Fig. 19, espectively. When the dynaic evese oent is applied, the thickness eduction atio is less than 12.5% in all angle anges (i.e ), as shown in Fig. 18. Theefoe, pipe ovality does not occu, as shown in Fig. 19.

7 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 DECEMBER 2011 / 1057 Fig. 19 Pipe shape siulated when a dynaic evese oent is applied Fig. 21 Appaatus fo high fequency induction heating and dynaic evese oent Table 8 Expeient condition fo pipe bending Paaetes Values Paaetes Values Mateial A106 G.B Heat width() 14 Pipe size 6 S40 Revese Dynaic oent oent Out diaete Tepeatue gadient 80 Thickness () 7.1 Heat tepeatue 980 D/T 23.7 Feeding velocity 40/in Fig. 22 Photogaph of the pipe-bending poduct (a) Angle befoe sping-back (b) Angle afte sping-back Fig. 20 FEA esults of bending angle consideed sping-back 3.5 Applying a Pipe bending Angle Consideed Sping-back Sping-back is consideed fo the optial pocess of the pipe bending. The pipe is bent by 90.9 because the sping-back angle given by Eq. (3) is 0.9 (section 3.2). The esult of FEA is that the bending angle afte sping-back is 90 when sping-back is consideed fo the bending pocess, as shown in Fig Expeiental Results and Consideation A pipe-bending test is pefoed to veify the optial pocess design by using the DOE ethod, the dynaic evese oent and the sping-back angle. The ateials and expeient conditions used fo pipe bending ae listed in Table 8, and the appaatus used fo high-fequency induction heating and application of the dynaic evese oent is shown in Fig. 21. The pipe-bending poduct obtained in the optial pocess designed on the basis of the data povided in Table 6 is shown in Fig. 22. The wall thicknesses easued using an ultasonic thickness gage fo diffeent angles ae in good ageeent with the FEA esults fo all pats of the pipe as shown in Fig. 23. Test Equipent : Ultasonic Thickness Gage, S/N : Wall thickness () Aveage Position eduction of thickness(%) Expeient 11.18% FEM (0%) (11.97%) (10.56%) (10.98%) (10.84%) (11.54%) (0%) (0%) 90 (11.97%) (11.69%) (11.83%) (11.69%) (11.69%) (0%) 11.77% Fig. 23 Copaison of wall thickness between expeient and FEA 5. Conclusions In this study, an optial pocess design fo the pipe bending by high-fequency induction heating (ρ/d = 1.5DR, D/t = 23.7) is poposed using the DOE ethod and a dynaic evese oent. 1. In the case of pipe bending with ρ/d = 1.5DR, the design facto that has the stongest effect on the thickness eduction atio is the evese oent (δ=3.02, Rank 1), and the effect of the othe factos is in the ode heating width (δ=2.79, Rank 2) > heating

8 1058 / DECEMBER 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 tepeatue (δ=1.32, Rank 3) > tepeatue gadient (δ=1.27, Rank 4) > feeding velocity (δ=0.07, Rank 5). 2. The diffeence between the thickness eduction atios at the two ends of the bent egion inceases with D/t. Theefoe, a dynaic evese oent is applied to obtain a unifo thickness eduction atio. 3. The sping-back angle is 0.9 ; it is obtained by using the FEA and theoetical analysis. The pipe is bent by 90.9 as a esult of sping-back. The esult of FEA is that the bending angle afte sping-back is 90, which satisfies the design citeia. The acceptable toleance of the pipe bending-angle is 90 ± In the case of pipe bending with ρ/d = 1.5DR, D = 168.3, t = 7.1, and D/t = 23.7, the thickness eduction atio is less than 12.5%, and ovality is pevented by using the DOE ethod, the dynaic evese oent and the sping-back angle. Pocess Design of the Hot Pipe Bending Pocess Using High Fequency Induction Heating, J. KSPE, Vol. 18, No. 9, pp , Ki, E. S., Lee, J. M. and Ki, B. M., The Shape Optiization of Washing Machine Shaft fo High-Speed Rotation though Analysis of Static and Dynaic Chaacteistics, J. KSPE, Vol. 25, No. 5, pp , Baek, S. Y., Kwon, J. W. and Lee, K. D., Effects of Blank Design Factos on Stetch Flange Foing of the Tailoed Blank Using Taguchi Method, Tans. Mate. Pocess, Vol. 9, No. 4, pp , ACKNOWLEDGEMENT This eseach was financially suppoted by the Ministy of Education, Science Technology (MEST) and Koea Institute fo Advanceent of Technology (KIAT) though the Huan Resouce Taining Poject fo Regional Innovation. And this wok is the outcoe of a Manpowe Developent poga fo Enegy & Resouces suppoted by the Ministy of Knowledge and Econoy (MKE). REFERENCES 1. Hu, Z. and Li, J. Q., Copute siulation of pipe-bending pocesses with sall bending adius using local induction heating, J. Mate. Pocess. Technol., Vol. 91, No. 1, pp , OKeefe, W., Inductive bending achine seeks to educe nube of welds in nuclea piping syste, Powe, Vol. 121, No. 12, pp , Hu, Z., Elasto-plastic solutions fo sping-back angle of pipe bending using local induction heating, J. Mate. Pocess. Technol., Vol. 102, No. 1-3, pp , Kuiyaa, S. and Aida, T., Theoetical analysis of bending of tube having unifo distibution of tepeatue by high fequency induction heating, Poc. of the 4 th Adv. Technol. of Plasticity, pp , Seong, D. Y., Jung, C. G., Yang, D. Y. and Chung, W. J., Efficient pediction of local failues fo etallic sandwich plates with pyaidal tuss coes duing the bending pocesses, Int. J. Pecis. Eng. Manuf., Vol. 12, No. 3, pp , Wang, Z. and Hu, Z., Theoy of pipe-bending to a sall bend adius using induction heating, J. Mate. Pocess. Technol., Vol. 21, No. 3, pp , Ryu, K. H., Lee, D. J., Ki, D. J., Ki, B. M. and Ki, K. H.,