CONICAL GAUSSIAN HEAT

Document Sample
CONICAL GAUSSIAN HEAT Powered By Docstoc
					International Journal of Mechanical Engineering (IJMET), ISSN 0976 – 6340(Print),
 International Journal of Mechanical Engineering and Technology
and Technology (IJMET), ISSN 0976 – 6340(Print), © IAEME
 ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010),    IJMET
ISSN 0976 – 6359(Online) Volume 1,
Number 1, July - Aug (2010), pp. 109-123                         ©IAEME
© IAEME, http://www.iaeme.com/ijmet.html

        CONICAL GAUSSIAN HEAT DISTRIBUTION FOR
             SUBMERGED ARC WELDING PROCESS
                                   Aniruddha Ghosh
                            Dept. of Mechanical Engineering
                      Govt. College of Engg. & Textile Technology
                                Berhampore, WB, India

                               Somnath Chattopadhyaya
                                  Dept of ME&MME
                                 ISM, Dhanbad, India

ABSTRACT:
        Studies on temperature distribution during welding are very important because
this may pave the way for application of microstructure modeling, thermal stress analysis,
residual stress/distribution and welding process simulation.
        An attempt has been made in this paper to predict of temperature variation of
entire plates during welding and after welding through an analytical solution is derived
from the transient three dimensional heat conduction of an infinite plate to finite
thickness. The heat input that is applied on the plates is exactly same amount of heat lost
for electric arc is assumed to be a moving heat source with Gaussian distribution. The
prediction was compared with experimental results with good agreement.
List of Symbols:
   α      =Thermal diffusivity(m2/s)
   c      =Specific heat(j/kg/K)
   Q      =Heat distribution
   Q0     =Net heat input per unit time(W)
   T      =Temperature of body(K)
   T0     =Initial Temperature of body(K)
   v      =Travel Speed (m/s)
   w      =Distance in x direction in a moving =coordinate of speed v (w=x-vt)(m)
   y      =Distance in y direction (m)
   z      =Distance in z direction (m)
   ρ      =Density(kg/m3)
   dQ     =Change of heat flux
   dT     =Change of temperature


                                           109
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


   dt       =Change of time
INTRODUCTION:
        More that forty years ago solution of a travelling point heat source for the case of
welding was first attempted. Then moving and stationary heat sources are frequently
employed in many manufacturing processes and contact surfaces. In recent years
application of localized heat source have been related to development of laser and
electron beams in material processing, such as welding, cutting, heat treatment of metals
and manufacturing of electronic components[1-2].Analytical and numerical models for
the prediction of the thermal fields induced by the stationary or moving heat sources
useful tools      for studying the afore mentioned problems[2].In some laser beam
applications, such as surface heat treatment, the contribution of convective heat transfer
must also taken into account[3].Quasi-steady state thermal fields induced by moving
localized heart sources have been widely investigated[3,4], whereas further attention
seems to be devoted to the analysis of temperature distribution in transient heat
conduction because temperature distribution has a significant influence on the residual
stresses, distortion and hence the fatigue behavior of welded structures. From literature,
presently many related work found. Classical solutions for the transient temperature field
such as Rosenthal’s solutions [5] dealt with the semi infinite body subjected to an instant
point heat source, line heat source or surface heat source. These solutions can be used to
predict the temperature field at a distance far from the heat source. Rykalin [6] pointed
out a heat flow model need to take the factors-non constant thermal properties, heat of
phase transformation, heat magnitude and distribution, plate geometry, convection and
surface depression in weld pool [7].Although Christensen’s experimental results indicate
that Rosenthal’s solution gives good agreement with the actual weld bead size over
several orders of magnitude, the scatter can be as much as a factor of three. The work of
Grosh [8] showed that that the effect of non-constant thermal properties can only make a
10-15 percent difference in the weld pool geometry, and Malmuth [9] has shown that the
effect of latent heat can only make a 5-10 percent difference. Obviously the heat input
magnitude solution of Rosenthal modified for non constant thermal properties and latent
heat can not explain the difference between theoretically predicted and experimentally
measured importance of the heat distribution on the plate surface. Fortunately several


                                                110
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


investigators have measured actual heat distributions in arcs on a water cooled copper
anode[10].Using these results it is possible to determine whether the presence of a
distributed rather than a point source of heat can explain the range of weld shape
variation measured by Chirstensen and others. It should be emphasized that this solution
retains all but one of the simplifying assumptions used by Rosenthal including absence of
convection in weld pool, constant thermal property, and no latent heat of phase
transformation. The only change in the use of a distributed rather than a point source of
heat. Inspite of these simplifications, it will be shown that the results not only agree with
the Rosenthal solution in the limit, but that they are capable of explaining most of the
experimental scatter. Rosenthal fail to predict the temperature in the vicinity of the heat
source [5]. Eager and Tsai [11] modified Rosenthal’s theory to include a two dimensional
(2-D) surface Gaussian distributed heat source with a constant distribution parameter
(which can be considered as an effective solution of arc radius) and found an analytical
solution for the temperature of a semi-infinite body subjected this moving heat source.
Their solution is a significant step for the improvement of temperature prediction in the
near heat source regions. Jeong and Cho [12] introduce an analytical solution for the
transient temperature field of fillet welded joint based the similar Gaussian heat source
but with different parameters (in two directions x and y). Using conformal mapping
technique, they have successfully transformed the solution for temperature field in the
plate of finite thickness to the fillet welded joint. Even though the available solutions
using the Gaussian heat sources could predict the temperature at regions closed to the
heat source, they are still limited by the shortcoming of the 2-D heat source itself with no
effect of penetration. This shortcoming can only be overcome if more general heat source
are implemented. Goldak, et al. (3-D)first introduced the three dimensional double
ellipsoidal moving heat source. Finite element modeling (FEM) was used to calculate the
temperature field of a bead-on-plate and showed that this 3-D heat source could
overcome the shortcoming of the previous 2-D Gaussian model to predict the temperature
of the welded joints with much deeper penetration. However, up to now, an analytical
solution for this kind of 3-D heat source was not yet available [13], and hence,
researchers must rely on FEM for transient temperature calculation or other simulation
purposes, which requires the thermal history of the components. Therefore, if any


                                                111
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


analytical solution for a temperature field from a 3-D heat source is available, a lot of
CPU time could be saved and the thermal-stress analysis or related simulations could be
carried out much more rapidly and conveniently. Nyguyen,et al.[14]are derived
analytical solution for the transient temperature field of the semi infinite body subjected
to 3-D power density moving heat source (such as semi-ellipsoidal and double ellipsoidal
heat source). However results based on           are not satisfactory semi-ellipsoidal 3-D heat
source with respect to double ellipsoidal heat source.
2. EXPERIMENTAL PROCEDURE
2.1 EXPERIMENTAL SETUP




Figure 1 MEMCO Semi Automatic Submerged Arc Welding machine at the workshop of
                     the Indian School of Mines, Dhanbad
2.2 SPECIFICATIONS:
Input voltage supply- 380/440 volts  Welding speed Trolley-30 to 1200 mm/min
3 Phase,50/60 Hz cycle, Air cooled   Wire feed speed-100 to 8000mm/min
Output current 600 amps              Wire diameter -2 to 5 mm
Duty cycle 100%                      Head movement vertical/horizontal -135 mm
Open circuit voltage 56volts, 35 Kva Deposition rate- 4 to 6 kg/hr
Flux hopper capacity 12.5 kg         Wire flux ratio-1:1
    • Flux used: ADOR Auto melt Gr II AWS/SFA 5.17(Granular flux)
    •    Electrode: ADOR 3.15 diameter copper coated wire
    •    Test Piece: 400 x 75 x1 6 mm square butt joint
    •    Weld position flat
    •    Electrode positive and perpendicular to the plate


                                                112
      International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
      ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


      2.3 PROCESS FLOW CHART:

Cutting of 20 mm Mild                Face Grinding on Automatic                 V-Groove preparation on
Steel Plate by Gas                   Grinding Machine                           Shaper Machine
Cutting



Grinding of the Face where                 Cutting of Samples by                 Welding by Submerged
further study is to be carried             Power Hack Saw                        Arc Welding Process
out



 Wax Coating of the Ground                  Removal of wax and                     Carbon coating on the
 Surface                                    cleaning of surface                    surface




                     Temperature reading taken on                       Study of bead geometry,
                     different points of welded plates by               estimation of dimensions of bead
                     laser non contact thermometer                      geometry

      SELECTING THE EXPERIMENTAL DESIGN
              The experiments were conducted as per the design matrix at random to avoid
      errors due to noise factors. The job 300x300x20 mm (3 pieces) was firmly fixed to a base
      plate by means of tack welding and then the welding was carried. The welding
      parameters were noted during actual welding to determine the fluctuations if any. The
      slag was removed and the job as allowed to cool down. The job was cut at three sections
      by hacksaw cutter and the average values of the penetration, reinforcement height and
      width were taken using vernier caliper of least count 0.02mm.Experimental procedure for
      prediction of Saw process: Same procedure as above, the job was cut at three sections and
      the average values of the penetration, reinforcement height and width (shown in fig. 2)
      were taken using vernier calliper of least count 0.02mm.




                                                      113
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME




        Figure 2 Bead geometry, P-Penetration-Reinforcement height-Bead Width

                 Table-1: Thermo physical properties of employed material
                  Thermal                Density(m3) Specific           Thermal
                   conductivity(W/m/ )                          heat(J/kg/ )       diffusivity(m2/s)

                               54                7861kg/m3            420              1.6×10-5
Steel(C=0.3%)
EXPERIMENTAL RESULTS:
                    Table 2 Set of reading obtained are tabulated as below
Sl.N   Volta     Curre     Travel    Penetrati    Reinforcem Wel          Weigh     Weigh      MDR
 o.    ge (V)    nt (A)     Speed       on            ent     d              t         t      (kg/mi
                           (cm/mi     (mm)        Height(mm Widt          (befor    (befor      n)
                             n)                        )      h              e         e
                                                             (mm          weldin    weldin
                                                               )            g)        g)
 1                                                           19.6          7.36      7.48
         25       350        17         6.67         2.74     8                                0.07
 2                                                           13.9           7.56     7.62
         25       350        30         5.26         1.02     5                                0.06
 3                                                           30.8           7.48     7.66
         25       450        17         7.65          3.8     8                                0.10
 4                                                           15.2           7.38     7.48
         25       450        30         6.52          2.1     8                                0.10
 5                                                           22.7           7.26     7.40
         35       350        17         6.02         1.91     6                                0.08
 6                                                           19.3
         35       350        30         5.90         1.80     2             7.33     7.41      0.08
 7                                                           25.7
         35       450        17         6.25         2.57     7             7.33     7.59      0.15
 8                                                           22.5
         35       450        30         6.02         2.13     3             7.32     7.49      0.17
        Explanation of Table 2-From literature [16] it is found that an increase in travel
speed substantially reduces the heat input resulting in lower burn off rate. This reduced
burn off rate decreases the metal deposition at the weld joint thereby lowering all the



                                                 114
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


three bead parameters i.e. penetration, reinforcement height and the width. It is seen that
the penetration increases with increase in the current, the reinforcement height also
increases marginally with an increase in the current but the width decreases i.e. it has a
negative effect. The increase in current results in decreasing arc length as well as
prevents the spreading of the arc cone; which results in higher melting temperature at the
tip and parent material, resulting in deeper penetration at the cost of bead width. The
decrease in bead width helps in marginally increasing the reinforcement height. There is a
small increase in the penetration but the effect on width is higher on the positive side.
The reinforcement reduces slightly.
        So above results are the interaction effects of input factors. From results of metal
deposition rate, we may get information about weld bead volume.
Table -3: Distribution of temperature on different grid points on the welded surface of the
     specimen for 7.87Kw heat input at 100th sec (at the end of the welding process,
                                   experimental values)
                       i
                j
                           1        2          3         4          5
                2            300.2    445.9      501.8     540.6      601.8
                1            450.7    501.5      545.9     610.5      713.1
                0            521.2    530.8      570.9     600.8      798.9
                -1           443.7    510.5      559.9     600.5      689.7
                -2           390.8    440.9      508.9     530.9      587.7

          Here x=ih, y=jk, h=0.075m, k=0.075m, Temperature reading taken in




Fig:3 A-Pictorial view of bell shaped Welding arc         Fig:3 B-Proposed ellipsoidal heat source
                                                          in which heat flux is distributed in a
                                                          Gaussian manner throughout the heat
                                                          source’s volume[14]




                                                    115
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME




Fig:3 C-Proposed spherical heat source in which       Fig:3 D-Proposed conical heat source in
heat flux is distributed in a Gaussian manner         which heat flux is distributed in a
throughout the heat source’s volume[5]                Gaussian manner throughout the heat
                                                      source’s volume
Figure 3 Heat source volume/shape in which heat flux is distributed in a Gaussian manner
                         throughout the heat source’s volume
DOUBLE CONICAL HEAT SOURCE:
          3-D heat source could overcome the shortcoming of the previous 2-D Gaussian
model to predict the temperature of the welded joints with much deeper penetration.
However, up to now, an analytical solution for this kind of 3-D heat source was not yet
available.
Let equation of a double cone 3-D heat source Gaussian model is
Q(x,y,z)=A[exp{-(x2+y2-(z+a)2×tan2β1)}+exp{-(x2+y2-(z-b)2×tan2β2)}]                                   (1)
Where A is amplititude of Gaussian distribution,(0,0,-a) position of electrode bottom
point,(0,0,b) penetration end point along z direction, β1, β2 are semi vertical angles of
cones .
For the case semi infinite Gaussian i.e. infinite length, breath but finite thickness then
equation will be
Qo=A                                                                                                  (2)

                             ,   taking tan2β1= tan2β2=1
The solution for the temperature field of semi-infinite body is based on the solution for an
instant point source that satisfies the following differential equation of heat conduction in
fixed coordinates

dTt’=                            ×exp (-                                   )                    (3)



                                                116
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


Where temperature rise dTt’ for a point heat source, dQ(the amount of heat located at
position (x’, y’, z’) at time t’) in a very small interval of time dt’. =thermal diffusivity; c
=specific heat; ρ=mass density.

Let us consider the solution of an instant semi-ellipsoidal heat source as a result of
superposition of a series of instant point heat sources over the volume of the described
Gaussian heat flux at a point source into Equation 3 and integration over the volume of
the heat source double conical heat source .

Let us consider the solution of an instant semi-ellipsoidal heat source as a result of
superposition of a series of instant point heat sources over the volume of the described
Gaussian heat flux at a point source into Equation 3 and integration over the volume of
the heat source double conical heat source .


dTt’=                           ×exp (-                                        )


For the case semi infinite Gaussian i.e. infinite length, breath but finite thickness then
equation will be

T-T0 =                                        × (2z+2k+ab)(0.8862×k0.5×                    +1) dk

[Where, k=4×α× (t-t’), so k=f (t’), w=(x-vt)]

=                                       × (2z+2k+a-b)(0.8862×k0.5×                    +1)dk        (4)



Solution of above Equation (4) has derived with the help of trapezoidal method for                       .
From this equation (4) temperature has calculated in different grid points at 100th sec for
travel speed 17cm/min and heat input 7.87Kw which are tabulated below are good
agreement with experimental results.




                                                117
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


   Table -4: Distribution of temperature on different grid points on the welded surface of the
     specimen for 7.87Kw heat input at 100th sec (just at the end of the welding process)
                      i
                  j
                             1          2           3          4          5
                  2               390        450        478         540        580
                  1               460        511        523         601        690
                  0               590        550        555         630        780
                  -1              460        511        523         601        690
                  -2              390        450        487         540        580
Here x=ih, y=jk, h=0.075m, k=0.075m, Temperature reading taken in                 .
        Both numerical and experimental results from this study have showed that the
present analytical solution could offer a very good prediction for transient temperatures
near the weld pool, as well as simulate the complicated welding path.
 Figure 5 Graphical representation for temperature distribution [data taken from table-4].




                                                118
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


Figure 6 Temperature values according to distance from welding nugget [data taken from
                                       table-4]




      Figure 8 Effect of weld current on temperature values [data taken from table-4]




                                                119
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


TEMPERATURE CALCULATION AFTER WELDING:




         Figure 9 Mesh grid for numerical solution two dimensional heat equation




Figure 10 Mesh grid for numerical solution two dimensional heat equation with nth plate
                       (for temperature calculation after time t)

Two dimensional heat equation is

     +      = ×                                                                                    (5)


                                                120
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


If h is step- size then mesh point (x,y,t) =( ih, hj, nl) or may be denoted as simply(i,j,n).
By applying Numerical method, Equation No. (5) Can be solved.
Solution:

     +      = ×

Or Ti,j,n+1 = Ti,j,n +(l/α×h2)[Ti-1,j,n + Ti+1,j,n +Ti,j+1,n + Ti,j-1,n - 4Ti,j,n]                 (6)
From Eqn. No. 4, 5, 6 and taking l=60 sec, h=0.075m, α=thermal diffusivity=9×10-6
m2/sec.Temperature of different grid points are calculated which are tabulated below;
these have good agreement with experimental values. Prediction of temperature on
different points on welding pates after welding has been made through this numerical
method .It is also newly found solution which will be very helpful to predict rate of
cooling of metal so hardness, heat affected zone etc.

Table -5: Distribution of temperature on different grid points on the welded surface of the
     specimen for 7.87Kw heat input at 100th sec (at the end of the welding process)

                         i
                  j
                             1          2           3          4          5
                  2               301        345        423         445        480
                  1               423        401        466         475        560
                  0               520        429        475         610        680
                  -1              423        401        466         475        560
                  -2              301        345        423         423        480

Here x=ih, y=jk, h=0.075m, k=0.075m, l=60sec, Temperature reading taken in                  .
         Here also both numerical and experimental results from this study have showed
that the present analytical solution could offer a very good prediction for transient
temperatures near the weld pool, as well as simulate the complicated welding path.

CONCLUSION:
         This type of numerical investigation is made to estimate two and three
dimensional transient heat conduction field in infinite and semi infinite metallic solid
because surface heat transfer strongly affected the temperature distribution in the welded
pates. In this study, analytical solutions for the transient temperature field of a semi


                                                121
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


infinite body subjected to 3-D power density moving heat source (such as double conical
heat sources) were found and experimentally validated. Also, it was shown the analytical
solution obtained for double conical heat source was a general one that can be reduced to
2-D Gaussian distributed heat source and classical instant point heat source. The
analytical solution for double conical heat source was used to calculate transient
temperatures at selected points on a mild steel plates which are welded by taking x- axis
along welding line, origin is starting point of welding, y-axis is perpendicular to welding
line and z-axis towards plate thickness. Both numerical and experimental results from
this study have showed that the present analytical solution could offer a very good
prediction for transient temperatures near the weld pool, as well as simulate the
complicated welding path. Furthermore, very good agreement between the calculated and
measured temperature data indeed shows the creditability of the newly found solution and
potential application for various simulation purposes, such as thermal stress, residual
stress calculations and microstructure modeling. At last prediction of temperature on
different points on welding pates after welding has been made through numerical method
.It is also newly found solution which will be very helpful to predict rate of cooling of
metal so hardness, heat affected zone.
REFERENCES:
[1] Tanasawa, I. and Lior, N., 1992, Heat and Mass Transfer in Material Processing,
    Hemisphere, Washington, D.C.
[2] Viskanta, R. and Bergman, T. L., 1998, Heat Transfer in Material Processing, in
    Handbook of Heat Transfer, Chap. 18, McGraw-Hill, New York.
[3] Shuja, S. Z., Yilbas, B. S., and Budair, M. O., 1998, Modeling of Laser Heating of
    Solid Substance Including Assisting Gas Impingement, Numer. Heat Transfer A, 33,
    pp. 315-339.
[4] Bianco, N., Manca, O. and Nardini, S., 2001, Comparison between Thermal
    Conductive Models for Moving Heat Sources in Material Processing, ASME HTD,
    369-6, pp. 11-22.
[5]Rosenthal, D. 1941, Mathematical theory of heat distribution during welding and cut-
    ting, Welding Journal20 (5), pp. 220-s - 234-s.



                                                122
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online) Volume 1, Number 1, July - Aug (2010), © IAEME


[6] Rykalin, N.N., and Nikolaev, A.V., Welding Arc heat Flow, welding in World, 9(3/4),
    1971, pp.112-132.
[7] Malmuth, N.D., Hall, W.F., Davis, B.I., and Rosen,C.D., Transent Thermal
    Phenomena and Weld Geometry in GTAW, Welding Journal 53(9),1974,pp.388s.
[8]Grosh,R.J., Trabant, E.A., Arc Welding Temperature, Welding Journal,35(3),1956, pp.
    396-s – 400-s.
[9] Lin, M.L., Influence of Surface Depression and Convection on weld Pool Geometry,
    Maters Thesis, MIT, Cambridge, MA, 1982.
[10] Nestor, O.H., Heat Intensity and Current Density Distribution at Anode of High
    Current Inert Gas Arcs, Journal of Applied Physics, 33(50,1967,pp.1638 – 1648.
[11] Eager, T. W., and Tsai, N. S. 1983, Temperature fields produced by traveling
    distributed heat sources, Welding Journal 62(12), pp.346-s - 355-s.
[12] Jeong, S. K., and Cho, H. S. 1997, An analytical solution to predict the transient
    temperature distribution in fillet arc welds. Welding Journal 76 (6), pp. 223-s - 232-s.
[13] Goldak, J., Chakravarti, A., and Bibby, M. 1985. A Double Ellipsoid Finite Element
    Model for Welding Heat Sources, IIW Doc.No. 212-603-85.
[14] Nguyen, N.T., Ohta, A., Suzuki, N.,Maeda, Y., Analytical Solutions for Transient
    Temperature of Semi-Infinite Body Subjected to 3-D Moving Heat Source, Welding
    Journal,August,1999,pp. 265-s – 274-s.
[15] Painter, M. J., Davies, M. H., Battersby, S., Jarvis, L., and Wahab, M. A. 1996. A
    literature review on numerical modeling the gas metal arc welding process, Australian
    Welding Research, CRC. No. 15, Welding Technology.
[16] Pillai et al. (2007) Some investigation on the Interaction of the Process Parameters
    of Submerged Arc welding, Manufacturing Technology & Research (An International
    Journal), Vol 3No.1&2, June-July.




                                                123

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:9
posted:11/19/2012
language:
pages:15