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Detecting Overheating in AM Parts using Computationally Efficient Thermal Models

Rajit Ranjan, Matthijs Langelaar, Can Ayas, Fred van Keulen

Structural Optimization and Mechanics (SOM)Delft University of Technology, The Netherlands

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Local Overheating in Additive Manufacturing

• Fusing successive layers of material on top of each other

• Certain geometries accumulate more heat

• Low local conductivity: improper heat evacuation

[1] Image source: http://www.mkstechgroup.com[2] Mertens et. al. Optimization of Scan Strategies in Selective Laser Melting of Aluminum Parts With DownfacingAreas.

Heat accumulation

Dross formation [2]

Powder

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[1] https://www.kmwe.nl/upload/file[2] Darya et.al 2017 Reduction of local overheating in selective laser melting[3] Adam et.al 2014 Design for Additive Manufacturing—Element transitions and aggregated structures

• Some more examples

Local Overheating in Additive Manufacturing

Vacuum seals manufactured by SLM [1]

Same overhang angle but different

overheating [3]

Upward curling due to longer thermal path to the substrate [2]

Thin section Thermal bottleneck

https://www.kmwe.nl/upload/file

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To develop an AM process model which can

1. Detect features causing heat accumulation in a given part geometry and is

2. Computationally efficient.

Objective

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Overview

Conceptual Understanding:1D Analytical study

Layer-by-layer part scale thermal model

(Computationally expensive)

Simplified models for estimating heat accumulation behaviour

Performance evaluated based on• Accuracy• Computational effort

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Overview

Conceptual Understanding:1D Analytical study

Layer-by-layer part scale thermal model

(Computationally expensive)

Simplified models for estimating heat accumulation behaviour

Performance evaluated based on• Accuracy• Computational effort

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Layer-by-layer thermal model• Element birth-and-death based lumped ‘layer-by-layer’ model [1]

• Exposure Time per layer = Laser scanning time• Heat source calculated based on energy equivalence

0T T

Maximum temperature for all time steps

‘Hotspot map’

• Temperatures indicates heat evacuation behaviour: Indicative fields

• Simplifications• Only conduction heat transfer• Conduction through powder not considered • Phase transformation not considered• Constant room temperature thermal properties for Ti-6Al-4V are used [2]

[1] Chuimenti et.al. 2017. Numerical modelling and experimental validation in Selective Laser Melting[2] Mujhkerjee et.al. 2018. Heat and fluid flow in additive manufacturing-Part I: Modelling of powder bed fusion

913

0

K

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Layer-by-layer thermal model

• Hotspot map for a complex part geometry

• Features with constant overhang angles• Different thermal behaviour!!

• Wall clock time: 43m 23s

Laser Power [W] 280

Absorption Coefficient 0.45

Scanning speed [m/s] 1.2

Recoater time [s] 10

Real layer thickness [mm] 0.1

Lumping factor 10

Key parameters [1]

180 mm

60

mm

[1] Chuimenti et.al. Numerical modelling and experimental validation in Selective Laser Melting

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Overview

Conceptual Understanding:1D Analytical study

Layer-by-layer part scale thermal model

(Computationally expensive)

Simplified models for estimating heat accumulation behaviour

Performance evaluated based on• Accuracy• Computational effort

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1D Heat Equation

Conceptual Understanding: 1D Analytical study

2

2

1T T

x t

Lx

2

2

1

21

( 1)( , ) ( , ) 2 sin

n tnh h L

n

n n

x xT x t T x e

L L

Method of separation of variables

2 2

2 2

1

21

( 1)( , ) 2 ( , ) (1 )sin

m h mt tmc h L L

m

m m

xT x t T x e e

L

Q

(2 1)

2n

n

(0, ) 0T t ( ,0) 0T x( ,0) ( , )h

hT x T x t

ht

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Observation 1: Only local domain matters

2

2

21

1( , ) ( , ) 1 2

n ht

h h Lh

n n

T L t T L e

• Only relevant domain can be considered if top(=maximum) temperatures arerequired

Q Q Q

1L

2L

3L

htSame and

2c hL t

1n

Graph created using 1000n

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Observation 2: Cooling is fast

x L• Cooling at topmost point i.e.

• Normalization ( , )ˆ ( , )( , )

c

c

h

h

T L tT L t

T L t

ht

2L

• Factors that influence cooling• Heating time• Characteristic time

2 2

2 2

2

2

( )

21

21

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( , )ˆ ( , )( , ) 1

1 2

m m h

m h

t t t

L L

cm mc

h th L

m m

e eT L t

T L tT L t

e

3max 10

• For our case, •

•

• Cools to 30% of max within first 2s

max 1ht

1000, 1 hn t

3

4

1

10

10

10

ht

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Observation 3: Steady state as an indicatorQ

L

ssQL

Tk

0T

• Steady state temperature also pick up low conductivity• Caution: no regard for local vicinity

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Overview

Conceptual Understanding:1D Analytical study

Layer-by-layer part scale thermal model

(Computationally expensive)

Simplified models for estimating heat accumulation behaviour

Performance evaluated based on• Accuracy• Computational effort

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Concept extension: Decoupling

• Layer-by-layer model

• Fast cooling between the layers• Therefore, we consider each layer addition starting at initial temperature

Maximum across all time

steps

Maximum across all geometry instances• Reduced wall clock time

• No cooling• Parallel computation

0T T 0T T 0T T

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Concept extension: Localization and Steady State

0T T 0T T 0T T

• Decoupled geometries (same as previous slide)

• Only domain close to heat deposition is relevant• Therefore, we only consider local domain given by

cL

• Transient• Steady State analysis

Maximum across all geometry instances

0T T0T T

0T TcL

cL

cL

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Results

Layer-by-layer

Decoupled layers

Maximum % err = 1.2Mean % err = 0.19

Steady state local analysis

Max = 11 %Mean = 1.8 % Decoupled and local layers

Layer-by-layer

Wall clock time 43m 23s

Qualitative match

Decoupled layers

6m 30s

Decoupled and localize

3m 38s

Steady state

43s

Maximum % err = 10.38 Mean % err = 1.4Max = 10.38 % Mean = 1.4 %

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Conclusions and Future work

• Developed a layer-by-layer model for detecting heat accumulation in AM parts.

• Significant computational gains achieved using 1D conceptual understanding• Valid for high fidelity part scale models as well

• Computational gain makes it possible to integrate with Topology Optimization method.

• In Progress:• Integration with Topology Optimization• Extension to 3D