Introduction of Prediction Method of Welding Deformation by Using Laminated Beam Modeling Theory and Its Application to Railway Rolling Stock

Transcription

1 IJR International Journal of Railway Vol., No. 4 / December 009, pp Introduction of Prediction Metod of Welding Deformation by Using Laminated Beam Modeling Teory and Its Application to Railway Rolling Stock Hyung-Suk Mun and Cang-Doo Jang Abstract Te welding deformation and its prediction metod at te HAZ (Heat-Affected Zone) are presented in tis paper. Te inerent strain metod is well known as analytical metod to predict welding deformation of large scale welded structure. Depend on te size of welding deformation in welding joints, te fatigue life, te stress concentration factor and te manufacturing quality of welded structure are decided. Many welded joints and its manufacturing control tecniques are also required to railway rolling stock and its structural parts suc as railway carbody and bogie frame. Proposed metods in tis paper focus on te two different te inerent strain area at HAZ. Tis is main idea of proposed metod and it makes more reliable result of welding deformation analysis at te HAZ. Keywords : Railway carbody, Heat affected zone Nomenclature b maximum breadt of te inerent strain region d maximum dept of te inerent strain region D deformation at te center k s Spring constant of te temperature cange region k b Spring constant of te adjacent region E b Young s modulus of te temperature cange region E s Young s modulus of adjacent region tickness of te plate m y moment on te welded line (Equivalent load) v b Poisson ratio of te temperature cange region v s Poisson ratio of te adjacent region Z section modulus α termal coefficient (1/) σ Yb yield stress of te temperature cange region r radial distance of disk ε total strain ε e elastic strain ε p plastic strain ε t termal strain ε tr pase transformation strain Corresponding autor: Korea Railroad Researc Institute smun@krri.re.kr RIMSE,Department of Naval Arcitecture & Ocean Engineering, Seoul National University ε inerent strain generated by te loading condition b 1 maximum breadt of te inerent strain region b maximum breadt of te eat equilibrium zone d 1 maximum dept of te inerent strain region d maximum dept of te eat equilibrium zone r 1 radial distance of te inerent strain region r radial distance of te disk eat equilibrium zone k 1 spring constant of te inerent strain region ε 1 inerent strain wit disk type and ring type area ε inerent strain wit ring type area ε inerent strain wit disk type area b z1 breadt of te inerent region b z breadt of te eat equilibrium zone E 1 Young s modulus of te inerent strain region E Young s modulus of te eat equilibrium zone E 3 Young s modulus of te adjacent region (plate area) m 1 Equivalent load at te inerent region m Equivalent load at te eat equilibrium region V Welding arc voltage[volt] I Welding current flowing between welding rod and base plate Q eat input per unit lengt V s welding speed F b transverse srinkage force of te adjacent region F s transverse srinkage force of te temperature cange region η welding effiency Vol., No. 4 / December

2 Hyung-Suk Mun and Cang-Doo Jang 1. Introduction Railway carbody and bogie frame ave many welded joints. Tese metal parts are jointed by eat and it permanently boned. Residual stresses at HAZ are caused by welding deformation. Te welding deformation negatively affects te required precision and stability of structural materials. For te last twelve years, among te metods used to predict welding deformations, te equivalent loading metod based on te inerent strain [1] as been successfully applied to calculate welding deformation due to its effective and reliable results. It is important to determine te inerent strain regions. Te inerent strain metod does tis by calculating te temperature distribution during welding [] and converting it into equivalent loads, from wic it is able to determine te deformation. Because tis metod independently generates a term related to te angular deformation, it can be applied very efficiently to precision deformation processes.. Inerent Strain in te HAZ Te total strain can be divided into te elastic, termal, plastic, and pase transformation strains, ε ε t + ε p + ε tr + ε e (1) F s k s x F b σ yb A ε x ε -- L F s Fig. 1 Force equilibrium in bar-spring model Fig. Force equilibrium in disk-spring model F b ε e σ yb E b (3) (4) (5) (6) Te inerent strain is defined as te irrecoverable strain after removing structural restraints and loads, or te sum of elastically irrecoverable strains tat induce permanent deformation of te material, + + ε ε e ε ε t ε p ε tr Typical inerent strains include plastic, termal, and pase transformation strains, i.e., te total strain wit te exception of te elastic strain [3]. A one-dimensional (1D) bar-spring model (Fig. 1) can be used to define te welded zone and te inerent strain caused by welding [4]. Te bar in Fig. 1 represents te temperature cange region wile te spring in represents te area of te welded zone wit te exception of te temperature cange region. Using a similar metod, Fig. uses a two-dimensional (D) plate-spring model to describe te welded zone conditions in more detail. Te D plate-spring model applies te coefficient and spring constant from te 1D bar spring model. Te spring model simulates te elastic restraint from te surrounding area outside te disk against te disk expansion and srinkage caused by a temperature cange. During temperature canges, te spring s restraining action induces an internal stress in te bar. Te inerent strain equation, () ε σ yb k s E b k b Eq. 4 indicates te external force acting on a bar by a spring equals a material s internal force. k b k s E b r ( 1 v b ) E s r ( 1 v s ) ε σ E yb 1 + v s b + 1 (10) E b E b 1 v s Based on te definition of te spring constants in Eq. 8 and Eq. 9, te D plate-spring model expresses te inerent strain as given by Eq Determining te Inerent Strain Region Te -D geometry of inerent strain region was introduced in Fig 3. And te result of computational eat conduction analysis was sown in Fig. 4. Maximum temperature on te bead modeling was considered of 300 o C [6]. Any area reacing temperatures (7) (8) (9) 176 IJR International Journal of Railway

3 Introduction of Prediction Metod of Welding Deformation by Using Laminated Beam Modeling Teory... Fig. 6 Organization of springs in HAZ Fig. 3 Heat transfer analysis and geometry of te inerent strain region above 700 o C during te welding process was defined as part of te inerent strain region [7]. Fig. 3 sows te maximum breat (b) and maximum dept (d) of te inerent strain region. Te geometry of te inerent strain region in FEM (Finite Element Metod) model is illustrated in Fig Determining te Equivalent Load Equivalent load in equation 11 was earned by substituting te geometrics values determined in Sections 3 [7] 1 m y b Fig. 4 Geometries of te inerent strain region Fig. 5 Distribution of te equivalent load along te welded line equation [7] E ε b z d z --E b z 6 b ε d 3π d -- (11) 5. Advanced Equivalent Loading Metod We discussed fundamental knowledge of conventional inerent strain metod in section 3. It was only considered inerent strain area and oter area. Tese areas were used to drive prediction formula of conventional welding deformation. But te main idea of advanced inerent strain metod is to define additional layer at te HAZ and applied its geometry dimensions to equivalent loading metod. Te additional area is defined between inerent strain and adjacent region is named eat equilibrium zone. Te advanced metod is considered te eat equilibrium zone as te adjacent area based on te region in te direction of its dept and its temperature dependence material properties. Te eat equilibrium area in advanced inerent strain metod is performed additional eat layer to calculate reliable inerent strain results. So tree different layers existed in advanced inerent strain metod suc as k 1, k, k 3. Te k is core teory of tis formula. k is in spring constant in eat equilibrium zone is divided into ring and disk types spring constants based on te springs restrictive conditions on te level of dept in HAZ [9] E 1 ε 1 z m y1 1 b 1 -- d 1 -- d 1 m y b 1 -- d 1 + ( )bz1 zdz ---- E ε _disk b z zdz -- d 1 E ε _ring ( b z b z1 )zdz (1) (13) Depend on definition te area of temperature canging zone at HAZ, equivalent load can be expressed as Eq. 1 and 13. Te total summation of te results from Eq. 1 and Eq. 13 are total equivalent load in HAZ in advanced inerent strain metod. Vol., No. 4 / December

4 Hyung-Suk Mun and Cang-Doo Jang Fig. 7 test specimen model Table 1 Welding Condition in Experimental Plate tickness I V V s η cm A V cm/sec % Fig. 8 All extruded aluminum carbody Table Comparison of te Experimental Results wit te Angular Distortion Analysis 6. Application te Equivalent Load to FEM Model or Simple Beam Formula Te welding deformation of te specimen can be calculated using te elastic analysis metod introduced by Jang et al. 1 and Nomoto et al. 8 It can also be calculated using a simple beam deflection formula. 7. Comparison of te Experimental Results wit Advanced Inerent Strain Metod Experimental welding condition was introduced in Table 1. Q VIη V s Angular Distortion (rad) Experimental results (1) Analysis results using te proposed ε () Analysis results using te conventional ε (3) FEM (4) (14) Fig. 9 Application of equivalent load to all extruded aluminum carbody Eq. 14 indicates tat calculation metod in eat flux in experimental welding line. Table gives te maximum deformation results from te experiment and te analyses measured at te central point of te specimen. Te results of te proposed metod gave us more reliable result tan conventional simple inerent strain metod. Conventional inerent strain metod was very limited to predict deformation at HAZ because it simply assumed inerent strain areas. 8. Application te Equivalent Load to Railway Rolling Stock Many railway rolling stocks are manufactured by welding process. But many assembled and welded railway rolling stocks ad been evaluated teir structural stability by using FEM witout considering post welding plastic and elastic mecanical properties of te line along welded jointed. As sown Fig 9, equivalent load can be applied to FEM model of all extruded aluminum carbody. And equivalent load was also applicable to te line along te welded joint to verify distribution residual stress in full assembled FEM model. 9. Conclusions We developed a new metod for calculating te inerent strain by incorporating te eat equilibrium area effects into te eat transfer analysis. Te following conclusions may be drawn. 1. An equivalent loading metod was introduced based on te inerent strain.. Main as advantage of inerent strain metod is not to require an elasto-plastic finite element analysis. 3. Te inerent strain metod tat incorporated te eat equilibrium area effects produced more reliable results tan te conventional metod. 178 IJR International Journal of Railway

5 Introduction of Prediction Metod of Welding Deformation by Using Laminated Beam Modeling Teory Te conventional inerent strain metod was only consider inerent strain area as temperature canging region but advanced metod consider additional eat equilibrium area to second temperature canging region at HAZ. It provide more accrue result Terefore, we can use te proposed inerent strain metod to predict welding deformation as well as its residual stress at welding joint of railway rolling stock. [1] Jang, C. D., Seo, S. I. and Ko, D. E. (1997), A study on te prediction of deformations of plates due to line eating using a simplified termal elasto-plastic analysis, Journal of Sip Production, Vol. 13, No. 1. [] Jang, C. D., Lee, C. H. and Ko, D. E.(00), Prediction of welding deformations of stiffened panels, Journal of Engineering for te Maritime Environment, Vol. 16, No. M. [3] Ha, Y. S. and Jang, C. D.(004), Developed inerent strain metod considering pase transformation of mild steel in line eating, Journal of Society of Naval Arcitects of Korea, Vol. 41, No. 6. [4] Jang, C. D., Kim, T. H. and Ko, D. E.(005), Prediction of steel plate deformation due to triangle eating using inerent strain metod, Journal of Marine Science and Tecnology, Vol. 10, No. 4. [5] Patel, B.(1985), Termo-elasto-plastic finite element formulation for deformation and residual stresses due to welds, P.D. Tesis, Carleton Univ., Ottawa, Canada. [6] Lee, J. H., Woo, J. H. and Rim, C. W.(001), Simulation of multi-layered welding process using ANSYS, ANSYS User s Conference. [7] Ko, D. E., Jang, C. D., Seo, S. I. and Lee, H. W.(1999), Real time simulation of deformation due to line eating for automatic ull forming system, Journal of te Society of Naval Arcitects of Korea, Vol. 36, No. 4. [8] Nomoto, T., Omori, T. and Sato, T.(1990), Development of simulator for plate bending by line eating, Journal of te Society of Naval Arcitects of Japan, Vol [9] Mun, H. S., Kim, T. K. and Jang, C. D.(009), Prediction of angular distortion of multi pass butt welding by inerent strain analysis based on laminated beam modeling for te inerent region and eat equilibrium zone, Spring Conference of Korean Society of Precision Engineering. [10] Yun, S. H., Jang, C. D., Kim J. T. and Mun, H. S., Analysis of post-weld deformation at te eat-affected zone using external forces based on te inerent strain, International Journal of Precision Engineering and Manufacturing, Vol. 8, No. 4, pp, Vol., No. 4 / December