Feedback Control of Melt Pool Area in Selective Laser Melting Additive Manufacturing Process
Abstract
:1. Introduction
2. Modelling
2.1. Analytical Lumped Parameter Model for Melt Pool Geometry
2.2. Energy Balance of Melt Pool Volume
2.3. Model Reduction
- a.
- The melt pool shape is assumed to be a half 3D ellipsoid as shown in Figure 2. If , and are the length, width, and depth of half ellipsoid, then the volume and cross-sectional area of the melt pool are given by and , respectively. The area of the melt pool interface with the substrate is given by and the area of the melt pool top surface is given by .
- b.
- These volumes and areas are further simplified by considering the constant width to length ratio of the melt pool defined as and the constant width to depth ratio of the melt pool defined as .Melt pool volume interfaces with the area of top free surface , and interfaces with the substrate are further expressed in terms of r and as:where , andwhere , andwhere .
- c.
- Melt pool temperature changes much faster than melt pool volume, so it is assumed that temperature reaches steady-state temperature and can be modelled with a constant percentage times the melting temperature as given in Equation (4).
2.4. Disturbance Model
3. Controller Design
3.1. Problem Formulation
3.2. Control Scheme
4. Results and Discussion
4.1. Open Loop Simulations Results
4.2. Closed Loop Simulations Results
4.2.1. Case 1: Disturbance due to Environment Temperature, Tini = 290 K
4.2.2. Case 2: Disturbance Due to Previous Tracks
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Symbol | Description |
---|---|
Volume of half ellipsoidal melt pool | |
Melt pool interface with the substrate | |
Melt pool interface with top free surface | |
r | Constant melt pool width to depth ratio |
β | Constant melt pool length to width ratio |
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Parameter | Value |
---|---|
Density: ρ | 8840 kg/m3 |
Thermal Conductivity: k | 9.8 W/m·K |
Thermal Diffusivity: a | 30,914 mm2/s |
Melting Temperature: Tm | 1568 K |
Specific Heat of Solid Inconel: Cp | 550 J/kg·K |
Specific Heat of Molten Inconel: Cp | 680 J/kg·K |
Solidus Temperature: Ts | 1290 K |
liquidus Temperature: Ts | 1350 K |
Latent Heat: Hf | 22,700 J/kg |
Absorption: η | 40% |
Convection Coefficient: αs | 2 × 105 W/m2·K |
Heat Transfer Coefficient: αG | 20 W/m2·K |
Temperature Ratio: μ | 0.2 |
Melt Pool Width to Depth Ratio: r | 1.75 |
Melt Pool Length to Width Ratio: β | 10 |
Case | Settling Time (s) | Rise Time (s) | Kp | Ki | Kd |
---|---|---|---|---|---|
Tini = 0 | |||||
Tini = 290 | |||||
Tini by Disturbance Model |
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Hussain, S.Z.; Kausar, Z.; Koreshi, Z.U.; Sheikh, S.R.; Rehman, H.Z.U.; Yaqoob, H.; Shah, M.F.; Abdullah, A.; Sher, F. Feedback Control of Melt Pool Area in Selective Laser Melting Additive Manufacturing Process. Processes 2021, 9, 1547. https://doi.org/10.3390/pr9091547
Hussain SZ, Kausar Z, Koreshi ZU, Sheikh SR, Rehman HZU, Yaqoob H, Shah MF, Abdullah A, Sher F. Feedback Control of Melt Pool Area in Selective Laser Melting Additive Manufacturing Process. Processes. 2021; 9(9):1547. https://doi.org/10.3390/pr9091547
Chicago/Turabian StyleHussain, Syed Zahid, Zareena Kausar, Zafar Ullah Koreshi, Shakil R. Sheikh, Hafiz Zia Ur Rehman, Haseeb Yaqoob, Muhammad Faizan Shah, Ahmad Abdullah, and Farooq Sher. 2021. "Feedback Control of Melt Pool Area in Selective Laser Melting Additive Manufacturing Process" Processes 9, no. 9: 1547. https://doi.org/10.3390/pr9091547