Research Papers

A Line Heat Input Model for Additive Manufacturing

[+] Author and Article Information
Jeff Irwin

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
17 Reber Building,
University Park, PA 16802
e-mail: jei5028@psu.edu

P. Michaleris

Associate Professor
Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802;
Pan Computing LLC,
State College, PA 16803

Manuscript received July 1, 2015; final manuscript received April 29, 2016; published online June 23, 2016. Assoc. Editor: Z. J. Pei.

J. Manuf. Sci. Eng 138(11), 111004 (Jun 23, 2016) (9 pages) Paper No: MANU-15-1327; doi: 10.1115/1.4033662 History: Received July 01, 2015; Revised April 29, 2016

A line input (LI) model has been developed, which makes the accurate modeling of powder bed processes more computationally efficient. Goldak's ellipsoidal model has been used extensively to model heat sources in additive manufacturing (AM), including lasers and electron beams. To accurately model the motion of the heat source, the simulation time increments must be small enough such that the source moves a distance smaller than its radius over the course of each increment. When the source radius is small and its velocity is large, a strict condition is imposed on the size of time increments regardless of any stability criteria. In powder bed systems, where radii of 0.1 mm and velocities of 500 mm/s are typical, a significant computational burden can result. The line heat input model relieves this burden by averaging the heat source over its path. This model allows the simulation of an entire heat source scan in just one time increment. However, such large time increments can lead to inaccurate results. Instead, the scan is broken up into several linear segments, each of which is applied in one increment. In this work, time increments are found that yield accurate results (less than 10% displacement error) and require less than 1/10 of the central processing unit (CPU) time required by Goldak's moving source model. A dimensionless correlation is given that can be used to determine the necessary time increment size that will greatly decrease the computational time required for any powder bed simulation while maintaining accuracy.

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Fig. 1

Illustration of the ellipsoidal heat distribution and the local heat source coordinate system with the origin at the start of the heating path. For vs > 0, the heat source moves in the local −z direction.

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Fig. 2

Temperature versus x location for two heat input models with different time increments compared to Goldak's model at the end of the third scan along the thermal line shown in Fig. 10: (a) line heat input models and (b) EE models

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Fig. 3

Power density versus global x location for two subsequent segments of a heat source scan using the EE model. The elongated length c̃ is chosen such that superposing these two segments gives a flat distribution.

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Fig. 4

Goldak's moving source (left) compared to LI (middle) and EE (right) power densities. LI and EE are scaled so that they are visible. Unscaled, their peak values are less intense than that of Goldak's model.

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Fig. 5

The mesh used to verify the heat input model, displacement boundary conditions (markers on the −x face), and heat source scans (lines on the +z face, not to scale). The hatch spacing between scans is 0.1 mm.

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Fig. 6

Schematic of the dimensions of the substrate (square outline) and laser scans (single-headed arrows), not to scale

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Fig. 7

Temperature-dependent material properties for Ti–6Al–4V

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Fig. 8

Temperature contours (°C) at the end of the first scan (top) and final scan (bottom)

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Fig. 9

Displacement contours (mm) magnified by a factor of 200 at the end of the first scan (top) and final scan (bottom)

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Fig. 10

Illustration of the point and lines at which the following results are shown

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Fig. 11

Longitudinal distortion (z displacement versus x location) for different heat input models at the end of the final scan along the longitudinal line shown in Fig. 10: (a) line heat input models and (b) EE models

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Fig. 12

Convergence study at node 1 for Inconel® 625 with a heat source speed of 450 mm/s (a) and CPU time reduction as a function of heat source speed for Ti–6Al–4V (b)

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Fig. 13

Temperature-dependent thermal and mechanical material properties for Inconel® 625

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Fig. 14

A correlation of the dimensionless parameters that can be used to find the necessary time increment, given material properties, and processing parameters

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Fig. 15

Sectioned view of the mesh, showing how the element sizes vary in the z direction




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