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Rapid Control Prototyping for the Production of Functionally Graded Materials with Tailored Microstructural Properties utilizing COMSOL Multiphysics J. Clobes, M. Alsmann, H.-J. Watermeier, H.-H. Becker, K. Steinhoff

WERK Kassel H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 2

Overview

1 Introduction

2 Extendible Control Architecture for Thermo-Mechanical Processes

3  Inductive Heating with COMSOL

4  Optimization of Process Specific Heating Strategies

5  Rapid Control Prototyping

6  Conclusion and Outlook

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Tailored Microstructural Components

Wear-optimized tailored components

Load-optimized tailored components

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 3

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Process Challenges

Heating Strategy

Radiative and

convective losses

Intra-billet heat flux

Source:  Me*orm  –  University  of  Kassel  

Transfer Forming Process Cooling Strategy

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 4

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FE Modeling

FEM Simulation

Maxwell equations:

Induced current density:

Coupled thermo-electrical system (intra-billet heat flux):

Simplifications:

•  2D axissymmetric model

•  Inclination of coils neglected

Geometry Coupled Differential Equations

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 5

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Model Verification

Specifications

power (Pind) = 18 kW

frequency (f ) = 8 kHz

time (tind) = 12 s

Time [s]

Tem

pera

ture

[°C

]

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 6

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Matlab and Comsol

Comsol Model Boundary Conditions

and Parameters

Simulation Output

FEM Based Control Architecture

Parameters

Control Parameters

Metal Forming Process

Mapping

SPS Control Architecture

Sensors and Actuators

FEM Verification

1. fem1.sol = asseminit(femmodel,

'init',femmodel.sol);

2. fem.sol=femtime

(fem,'init',fem1.sol, ...

,[…]);

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 7

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Numerical Optimization of the Heating Strategy Steepest gradient descent Genetic algorithm

Advantages and disadvantages: - Suited for complex, nonlinear problems - Stochastic search - Usually slower

Advantages and disadvantages: - Fast convergence - Requires gradient - Start-value dependent

Initial Population

Random Variation

Evaluation of Fitness

Apply Selection

Evaluate Cost Function

Determine Gradient (dk)

Update Ik[m]: Ik=Ik-1+αkdk

Cost function

Steepest Gradient Descent Genetic Algorithm

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 8

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above AC3

Strong Core-Surface Gradient Heating Strategy

r

z Time [s]

Tem

pera

ture

[°C

]

Radius [mm]

Tem

pera

ture

[°C

]

Heating Strategy Temperature Profile

0s  soaking  2s  soaking  6s  soaking  

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 9

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Rapid Control Prototyping

Source: D. Abel and A. Bollig, Rapid Control Prototyping, Springer 2006

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 10

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Fuzzy Logic Controller

Fuzzy Logic Control Online Adaption

"↓$%$& =[█■0&0&0&0&0&0&0@0&0&0&0&0&0&0@0&0&0&0&0&0&0@0&0&0&0&0&0&0@0&0&0&0&0&0&0@0&0&0&0&0&0&0@0&0&0&0&0&0&0 ]

-

.-

No pirior process information

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 11

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Simulative Evaluation of Cycle Time Impact

20ms cycle time

50ms cycle time

250ms cycle time

Time [s]

Time [s]

Time [s]

Tem

pera

ture

[°C

] Te

mpe

ratu

re [°

C]

Tem

pera

ture

[°C

]

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 12

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Application Results

Fuzzy Controller development utilizing

Comsol

Fuzzy Controller optimization utilizing Comsol

Direct translation into C-code with no alterations

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 13

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Conclusion and Outlook

Conclusion - Control of highly nonlinear system - Complex optimization algorithms - Implementation of complex, self adjusting control algorithms

Opportunities: - Highly flexible production system for high precision mass customization - Stable, tailored product quality properties (dimensions, microstructural distribution, etc.) - Adaptable to all thermo-mechanical processes

Future Challenges: - Multi-form flanged shafts - Complex geometries - Mapping to sheet metal forming

Source: Institute of Mechanics –Chair of Numerical Mechanics

H – Dipl.-Ing. J. Clobes – Tel.: +49561 49059541 – Stand: 25.10.2011 – 14

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Thank you for your attention!