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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
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2
1T T
x t
Lx
2
2
1
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( 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