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Physics Based Modeling for Economic Assessments

By Jerry Gould on Friday, February 17th, 2012

Welding exists in the world of manufacturing as a cost effective vehicle for the production of increasing complexity components.  If welding was not the cost effective solution, than some other technology or technologies would be dominant where joining is predominant today.  Of course, variants of welding and joining continue to proliferate as the science of these technologies advances.  This results in technologies that can both enable new products, and be increasingly economically competitive.  With such a wide array of joining (and other) approaches to choose from, it has become increasingly difficult to understand how to identify best candidates, and to define the economic advantages of these methods.  This is further complicated by candidate applications for which a technical concept is forwarded, but no related assembly technology is defined.  At EWI, there is an ongoing effort to develop tools for conducting such economic analyses.  These tools are physics based models adapting the suggested process technology to a specific application.  An example can be taken from recent work done at EWI assessing a new generation of continuous resistance brazing.  This was intended for an end application fabricating low cost honeycomb panels.  Continuous resistance brazing offers potential for high speed consolidation, with resulting cost reductions in the final product.  Before work was undertaken to fully develop this technology, physics based modeling was used to understand potential constraints of the approach.

Figure 1 – Conceptual Overview of a Continuous Resistance Brazing Line. The line includes two rolls with current passed across the roll faces. Heating of the strip is then done through contact.

 The continuous resistance brazing concept is diagrammed in Figure 1.  The process incorporates two rolls, and a power source that allows current to be passed across the face of each roll creating the resistance heating necessary for brazing.  That heat is then conducted into the workpiece by contact conduction.  Physics based modeling of this process was done by considering thermal and electrical components to the technology.  The thermal aspect addressed conducting heat from the rolls into the workpiece along the contact length.  This was done by combining one dimensional heat transfer solutions (one for the roll, the other for the strip workpiece) and examining subsequent temperature variations at the strip center.  Two equations, one for heating and the other for subsequent cooling, have been developed. 

On heating:


 On cooling:


Examining these equations allowed conditions to be defined for achieving both steady state temperature of the strip.  An example of a typical temperature profile defined from these equations is shown in Figure 2.  The temperature data is shown as a function of distance from initial contact with the roll. 

Figure 2 – Typical Temperature Variations at the Center of the Workpiece Strip for Continuous Resistance Brazing. This plot is for a roll temperature of 600oC. Temperature is shown as a function of distance from initial strip contact with the roll.

Such temperature data was then used to establish relationships between workpiece geometry and maximum processing speeds.  These results are shown in Figure 3.  From these results, it is clear that the thinnest workpieces of interest (1.5-mm overall thickness) showed potential processing speeds in excess of 10-m/min.  Processing speeds fell rapidly, however, for heavier workpiece sections.

Finally, the developed processing speeds and design of the roll could be used to define power requirements for continuous resistance brazing.  For the geometry described, roll current and voltage can be defined through the following equations:

Figure 3 – Maximum Line Speeds for Continuous Resistance Brazing as a Function of Workpiece Geometry.


From these equations, power demands (including both current and voltage) can be defined as a function of processing speed and workpiece width.  These results are shown in Figure 4.  These results show the increasing power demand of both increases in processing speed and strip width.

Analyses such as these demonstrate the utility of physics based modeling for understanding the economic implementations of new generations of welding technology.  Such examinations allow potential costs and economic benefit of new technologies to be assessed in a rudimentary way, defining best candidate approaches for further investment.  EWI now commonly carries out such analyses for its customers.  These analyses have been used to allow down-selection of candidate technologies early in development processes, maximizing return on research investment funds.

Figure 4 – Current and Voltage Demands for Continuous Resistance Brazing a Nominal 1.5-mm Product. Results are shown for strip stock ranging from 150-mm to 2000-mm wide.

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