This document presents a bond graph approach to model gas metal arc welding (GMAW). It summarizes existing static force balance and modified force balance models used to estimate droplet sizes in GMAW. It then describes modeling the welding process using magnetohydrodynamic equations and developing a hydraulic bond graph model to represent the droplet formation process. Key components of the bond graph model include fluid inertances, capacitances and resistances to model the forces involved and predict droplet volume over time. Simulation results show the model volume output is within 50% error of the theoretical volume curve.

1. Presentation on
A Bond Graph Approach to Model
Gas Metal Arc Welding(GMAW)
Presented by:
Abhay Singh Rana
M.E. CAD/CAM Engineering
Roll No: 851281001
1
Under The Guidance of
Dr. Tarun Kumar Bera
Associate Professor
Department of Mechanical Engineering
Thapar University, Patiala

2. Introduction
• Estimation and control of droplet sizes in Gas Metal Arc Welding (GMAW)
is an application of Magneto hydrodynamic systems.
• Two approaches being used are SFBM (Static Force Balance Model) and
MFBM (Modified Force Balance Model).
• SFBM quite accurately [1] predicts the radius of globular mass transfer drop
with the force equilibrium equations. Where surface tension is to be equal
to gravitational and electromagnetic forces.

3. Literature Survey
Sl
No.
Author Publication Publisher Key Points
1 Nabeel Arif, Jae
Hak Lee and
Choong Don Yoo
Modeling of
globular transfer
considering
momentum flux
in GMAW
IOP Publishing
Journal of
Physics D:
Applied Physics
Basic Introduction of the
equilibrium models.
Characteristic Curves of
forces, with current and
arc angle.
2 L A Jones, T W
Eagar and J H
Lang
Magnetic Forces
acting on molten
drops in gas
metal arc
welding
J. Phys. D:
Appl. Phys.
Derivation of the
expression for the
electromagnetic force,
Film of Droplet formation.

4. Literature Survey
3 C . Sozou and W.
M. Pickering
The
development of
magnetohydrody
namic flow
due to an
electric current
discharge
Journal of fluid
mechanics
Modeling in
magnetohydrodynamic
domain
Problem Formulation
with numerical
methods (Introduction
to Magnetic Diffusion)
4 W J Greene An Analysis of
Transfer in Gas-
Shielded
Welding Arcs
AIEE Basic derivation of
Electromagnetic Force

5. Literature Survey
5 J.F. Lancaster The physics of fusion
welding
Part 1: The electric arc in
welding
IEE REVIEW Basics of Welding
6 J. C. Amson Lorentz force in the
molten tip of an arc
electrode
Brit. Journal of
Applied Physics
(IOP Publishing)
Complete
derivation of
Lorentz force and
proof of
assumptions.
7 P. M. Heertzes,
L. H. de Nie and
H. J. de Vries
Drop formation in liquid-
liquid systems - I
Prediction of drop
volumes at moderate
speed of formation
Chemical
Engineering
Science,
Pergamon Press
Basic equations for
water drop
detachment.

6. Literature Survey
8
9
10

7. SFBM Model
• Drop is detached when Surface tension force is equal to sum of forces due to
gravity, drag and electromagnetism.
• (1)
• The problem with SFBM is that when at large currents the error starts to get large,
hence the necking phenomenon is also considered through Pinch Instability
Theory (PIT).
• Model is valid in case for arc lengths greater then the diameter of the radius of
electrodes.
• It fails when short circuiting is involved.

8. • When momentum flux forces increase on higher currents, SFBM does not give
accurate results, so MFBM is used.
• (2)
• For very accurate results numerical techniques are used[3][4].
Results are far more accurate then any analytic technique

9. Legend
1) Rw =Radius of Wire
2) I=Supplied Current
3) P1=Plane 1
4) Ra=Droplet Radius
5) U=Flow Velocity
6) J0=Current Density
in zero current
emission density
region
7) J2=Current Density
on plane p2
8) J=Constant current
density in truncated
sphere
Figure.3 Globular Droplet, With pressure, currents and Planes [1]

10. • (4)
• α=Ratio of diameter of droplet and diameter of wire.
• α is an useful parameter to vary in order to recognize mode of transfer i.e.
Globular/Spray.
Force due to Mass Transfer(Fmf)

11. Electromagnetic Force

12. • Resulting electromagnetic force:
(3)
• In Figure. X Lorentz force of the cone A is independent of apex angle, hence that
cone is depicted as plane 1 in the figure. X1 and the zero current emission density
zone is considered to be below plane P2, having X-sectional area of electrode
wire.[1][3]

13. Magnetohydrodrodynamics
• In MHD Maxwell equations are coupled with Navier Stoke’s Equations to find out
the variance of 9 variables i.e. 3 components of Velocity(V),3 components of
Magnetic field(B) and thermodynamic properties ( density, pressure and internal
energy)
• Final Equilibrium equation gives the relation between the 9 variables in ideal MHD.
• Causal difference between Electrical engineering Approach and MHD approach.

14. Equilibrium Equations
• Equilibrium equation for Numerical Analysis

15. Legend for Characteristic curves
• Fd= Drag Force
• Fg= Gravity Force
• Fem=Electromagnetic Force
• Fmf= Force due to Momentum Flux
• Ft= Detaching Force
• Fγ= Surface tension force
• Figure. 4 show the behavior of Fem and Fmf against arc covered angle.Figure.5
shows the current at which detaching force equals Surface tension force

16. Characteristic Curves for MFBM
Models[1]
Fig. 4 Plot of EM force with arc angle[1] Fig.5 Detaching Force with Current[1]

17. Photographs of Melting Drop[4]
Fig. 6 Process of Droplet detachment at 260 Amp and 29 V in 1.6 mm φ electrode[2]

18. Analogy to hydraulic System
• Carefully looking at Fig.6 and not considering the electromagnetic force.
Droplet detachment can be seen as water drop detachment with low velocity and
uniform acceleration
This dictates the basic premise of modeling, where scheme is to model the
hydraulic circuit and pass it on to magnetic domain by use of a suitable Gyrator.

19. Figure.7 Detaching Water Droplet[Google Images]

20. • If we look closely in that figure we can approximate upper part of the fluid in drop
growth stage, as a truncated cone and the lower part as an truncated sphere.
The hydraulic bond graph model is prepared, with these simplifications, we can say
that the necking phenomenon is taken into account as the top part is truncated
cone, but it is far from ideal as rn is not changing

21. Nomenclature Used in Bond graph
• Radius at necking
• Radius of the drop
• Volume flow rate
• Magnetic Permeability
• Magnetic field Intensity H
• Surface tension Co-efficient γ
• X-sectional Area A(x)
• Shoulder Angle θ

22. Hydraulic Bond Graph Modeling
• Fluid Inertance: It is defined as “The pressure difference required for a unit flow
rate change”.
• (4)
• (5)
(6)

23. Fluid Capacitances
• The capacitance reflects storage capacity and is given as the ratio of the volume
flow rate and the rate of pressure variation.
• (7)
• In the same way
• (8)

24. Fluid Resistances
• Basic model is taken as inviscid, so viscous resistances are neglected.
• Bernoulli’s Resistance which represent the pressure variations with varying X-
sectional area is used. These are Modulated Resistances.
• (9)

25. Bond graph
Fig.8 Bond graph of drop detachment model

26. Input Radius
Plot.1 Input radius (drop)

27. Theoretical Volume
Plot.2 Desired Volume Curve.

28. Model Volume output
Model Volume output is within 50 percent error with respect to theoretical volume
Plot.3 Actual Volume Curve