Process Modeling

Lesson ObjectivesWhen you finish this lesson you will understand:• The various modeling techniques listed below

Learning Activities1. View Slides; 2. Read Notes, 3. Listen to lecture4. Do on-line

workbook

KeywordsElectro-thermal Modeling, Thermo-mechanical Modeling, Electrode Modeling, Surface Contact Modeling, Solidification Modeling, Process Control Modeling, Law of Thermal Similarity, Machine Characteristics Modeling

Modeling Efforts

• Electrothermal Modeling• Nugget Growth• Electrode Design• Expulsion

• Thermomechanical Modeling• Stress Analysis

• Electrode Modeling • Electrode Life• Electrode Misalignment

• Surface Contact• Solidification• Process Control

• Law of Thermal Similarity• Machine Characteristics

Resistive Current Path “Breakdown” Model

Liang, “Foundational Study of Contact Behavior..”,OSU Dissertation, 2000

IRW Tech Catalog, Rel #2, Jan 1999

Model for Heat Generation - Electrode Face

Alcan A-Nose

Electrode Design - Heat Generation

A Model For Expulsion Prediction

Modeling Efforts

Model of stress

Modeling Efforts

Model of Heating for Electrode Misalignment

Modeling Efforts

• Surface Contact• Melting &Solidification• Process Control

A heat balance problem is set up when welding Steel to Aluminum Using a Transition Material of Roll Bonded Al to Steel Sheet.

Heat Balance

Aluminum

Steel-AlTransition

Move to Next Slide to See Nugget Growth

Results and Discussion(nugget development model)

One CycleTwo CyclesThree CyclesFour CyclesFive CyclesSix CyclesSeven CyclesEight CyclesNine CyclesTen CyclesEleven CyclesTwelve Cycles

Modeling Efforts

0.1 Sec

10 sec

Law of Thermal Similarity

Temp at x0 at t0 = Temp at n*x0 at n2*t0

Temp at 1mm, 0.1 sec = Temp at 10 mm, 10 secOkuda, T. Law of Thermal Similarity,Mitsubishi Electric 1973

Law of Thermal Similarity

Okuda, T. Law of Thermal Similarity,Mitsubishi Electric 1973

“For the case where the plate thickness and the diameter of the electrodes are magnified by n times, if we also change the current density by 1/n times (which is current by n times), and heating time by n2 times, the new temperature distribution becomes similar to the original one”

n=6n2 = 368 * 36 = 288

Okuda, T. Law of Thermal Similarity,Mitsubishi Electric 1973

Measurement of melted and partially melted thicknesses using picral etch

Thickness not melted

Melted & solidified weld

nugget

Partially melted zone

Nugget

Fong & Tsang “Law of Thermal Similarity”Senior Project, OSU, 2000

Measurement of Heat affected(HAZ) and non-heat affected (N-HAZ) melted

thicknesses using Nital etch

Non-recrystallized thickness (N-HAZ)

Recrystallized thickness (HAZ)

Law of Thermal Similarity Applied to Stacks of Mild Steel Sheet

Thinnest Outer Sheet

Sum of All Thickness

Optimum Weld Time Example

Optimum weld time for 1.25 sheet welded to itself = 8 cycles

Total thickness welded with this combination = 2.5 mm

Optimum weld time for different thickness combinations can be derived from the following equation:

*optimum weld time for the experimental thickness = weld time for new thickness

2)_exp

_( thicknesserimental

thicknessnew

Calculate Time Constant for unit thickness 1mm to 1mm

(for 1.25mm – 1.25mm = 8 cycles)

2)_exp

_( thicknesserimental

thicknessnew *optimum weld time for the experimental thickness = weld time for new thickness

cyclescyclesmm

mm58*)

Thick/thin and multi-sheet welding

Combination 1

2.5 mm sheet welded to 1.25 mm sheet

Combination 2

3 sheets of 1.25 mm thickness each welded together

Verification – Thin-Thick sheet• Total thickness welded for combination 1 = 3.75 mm• Weld time for combination 1 = (3.75/2.5)2*8 = 18 cycles• Weld time for any single welding pulse can not exceed 8 cycles; cooling times need to be added and pulsed welding done to keep thin sheet from overheating

• Weld schedule = 7 cycles weld + 4 cycles cool + 7 cycles weld (total time = 18 cycles)

Note: weld time reduced from 8 cycles to 7 cycles for each pulse to fit in within the total weld time.

Verification – Thin-Thick sheet

Weld nugget is evenly distributed in the thick/thin sheets

Thin sheet is not overheated and the nugget is symmetrical with the two outer surfaces

Verification – 3 Sheet Combination

• Total thickness welded for combination 2 = 3.75 mm • Weld time for combination 1 = (3.75 /2.5)2*8 = 18 cycles

• Weld time for any single welding pulse can not exceed 8 cycles; cooling times need to added and pulsed welding needs to be done

• Weld schedule = 7 cycles weld + 4 cycles cool + 7 cycles weld (total time = 18 cycles)

Note: weld time reduced from 8 cycles to 7 cycles for each pulse to fit in within the total weld time.

Verification – 3 Sheet Combination

Weld nugget is evenly distributed in the 3 sheet combination as well

Good sized nugget without overheating surfaces

Modeling Efforts

Machine Characteristics - Regions to Model

Mechanical Models to Characterize Machine

Model 2Bouncing Region

Model 3 Welding Region

Ball Test Results to Confirm Bouncing Region Model

After the first bounce, the model predictionin brown fits well to the experimental data in black.

Process Modeling

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