1. Estimation of the Characteristic Properties of the Weld Pool during High Productivity Arc Welding Dr. Patricio Mendez Prof. Thomas W. Eagar Massachusetts Institute of Technology October 4th, 1999

2. 2 High Productivity Welding high current high speed Good welds Bad welds increased productivity Good Weld Bad Weld (humping) Top view Cross section beginningend Top view Cross sections beginning end (undercutting) Savage et al., 1979

3. 3 Outline Description of the problem and current understanding Methodology Formulation of the problem Results and discussion

4. 4 Geometry of the Problem The productivity limiting defects are associated to a very depressed weld pool. (Bradstreet, 1968; Yamamoto, 1975; Shimada, 1982; Savage, 1979) gouging region trailing region gouging region rim

5. 5 Possible Causes for Depression Marangoni Forces: they are dominant at lower currents (Heiple and Roper, 1982; Oreper and Szekely, 1984; etc.). Electromagnetic Forces: they increase with current. Arc Pressure: exerts a direct action on the free surface (Weiss et al., 1996; Lin and Eagar, 1983; Rokhlin and Guu, 1993). Gas Shear on the Surface: increases with current (Ishizaki, 1962; Choo and Szekely, 1991). How to determine the dominant force in such a complicated geometry?

6. 6 Methodology: Order of Magnitude Scaling Features: –Acts as a bridge between dimensional analysis and asymptotic considerations. –Includes all of the desired driving forces. –Uses the governing differential equations. –Previous insight into the problem is especially relevant. –Output: set of order of magnitude scaling factors for the solution of the problem determination of the relative importance of different driving forces and effects generalization of results from calculations or experiments

7. 7 Elements of Order of Magnitude Scaling Normalization Functional requirements (Domain partition) Asymptotic considerations This is applied to the governing equations

8. 8 This normalization generates dimensionless functions of the order of magnitude of one. Normalization 01 0 1 AB F(A)F(A) F(B)F(B) X x F(X)F(X) f(x)f(x)

9. 9 The second derivatives must be of the order of one This condition assures that the first derivatives are also of the order of one. OKnot OK This is a new condition not mentioned in other references Limitation: equations of second order or less Functional Requirements

10. 10 Functional Requirements: Domain Partition Choosing the appropriate domain the second derivatives are of the order of one. The size of the partition might be initially unknown. domain of problem subdomain for scaling Limitation: many subdivisions may make the process more difficult instead of simpler

11. 11 The unknown functions can be replaced by functions of the order of one with unknown scaling factors: unknown function unknown scaling factor dimensionless function  1 Asymptotic Considerations: Extraction of Algebraic Equations from Differential Ones

12. 12 Dominant balance is used for the normalization of the differential equations. The normalized differential equations are transformed into algebraic equations: 1 differential equation 1 algebraic equation: 11 11 Asymptotic Considerations: Extraction of Algebraic Equations from Differential Ones

13. 13 Matrix Algebra Dimensional Analysis Differential Equations Asymptotic Considerations inspectional analysis similarity Szirtes 1998, Chen 1971, Barr 1987 Bender and Orszag, 1978 dominant balance characteristic values Denn, 1980 intermediate asymptotics Chen, 1990; Barenblatt, 1996 Related Techniques

14. 14 Formulation of the Problem 2-dimensional formulation, quasi-stationary traveling weld. Focus on depressed part of weld pool. Driving forces included: –Gas shear on the free surface –Arc pressure –Hydrostatic pressure –Capillary forces –Marangoni forces –Buoyancy forces

15. 15 Formulation of the Problem 9 Unknowns: –  (X), U(X,Z), W(X,Z), P(X,Z), T(X,Z) –  (X,Z), J X (X,Z), J Z (X,Z), B(X,Z) 8 Estimations –  *, U*, W*, P*, T*,  *, J*, B* 9 Equations: –mass conservation, Navier-Stokes(2), energy conservation, Marangoni. –Ohm (2), Ampere (2), charge conservation.

16. 16 Formulation of the Problem 17 Parameters: –L, , , k, Q max, J max,  e, g,,  T, , P max,  max, U ,  0, ,  s 7 Reference Units: –m, kg, s, K, A, J, V 10 Dimensionless Groups –Reynolds, Stokes, Elsasser, Grashoff, Peclet, Marangoni, Capillary, Poiseuille, geometric, ratio of diffusivity

17. 17 Results: estimations U*U* ** **

18. 18 Results: gas shear is the dominant driving force arc pressure / viscous electromagnetic / viscoushydrostatic / viscouscapillary / viscousMarangoni / gas shear buoyancy / viscous gas shear / viscous convection / conduction inertial / viscous diff. = /diff.  N2N2 N5N5 N8N8 N 24 N 26 N6N6 N7N7 N 27 N 15 1

19. 19 Discussion The driving forces previously suggested as possible causes for the big depression include: –Electromagnetic forces: they are not dominant, because they tend to raise the surface instead of creating a depression (Tsai and Kou, 1989) –Arc pressure: is not dominant, because it is too small to create the observed depression (Lin and Eagar, 1985; Rokhlin and Guu 1993) –Marangoni: experiments were conducted on 304 stainless steel with high (230 ppm) and low (6 ppm) sulfur content.

20. 20 Marangoni effect is of little importance

21. 21 Conclusions In the high productivity regime: –Arc shear on the free surface is the dominant driving force in the weld pool. –The weld pool degenerates into a thin liquid film. –The observed depression is approximately equal to the weld penetration. –The order of magnitude of the dimensionless groups obtained suggests that some terms in the governing equations could be simplified in more detailed calculations.