Automatic determination of part build orientation for laser powder bed fusion

Figures & data

Figure 1. Schematic diagram of the LPBF process.

Figure 2. Framework of the proposed build orientation determination method.

Figure 3. Schematic diagram of an optimal orientation selection approach.

Figure 4. An illustration of the volumetric error of a facet.

Table 1. An explanation of the symbols in the estimation model of build time.

Symbol	Meaning	Unit	Value
$h_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}^O$	STL model height in O	mm	Calculate according to the STL model and O
$t_{\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}}$	Layer thickness	mm	Specify based on the technical data of the used machine
$T_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}}$	Recoating time	s	Specify based on the technical data of the used machine
$V_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}$	STL model volume	${\mathrm{m}\mathrm{m}}^3$	Calculate according to the STL model
$V_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}}^O$	Support volume in O	${\mathrm{m}\mathrm{m}}^3$	Estimate using the Autodesk Meshmixer software
$s_{\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}$	Hatch spacing	mm	Specify based on the technical data of the used machine
$v_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}}$	Laser scanning velocity	mm/s	Specify based on the technical data of the used machine

Table 2. An explanation of the symbols in the estimation model of build cost.

Symbol	Meaning	Unit	Value
$V_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}$	STL model volume	${\mathrm{m}}^3$	Calculate according to the STL model
$V_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}}^O$	Support volume in O	${\mathrm{m}}^3$	Estimate using the Autodesk Meshmixer software
$r_{\mathrm{w}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{e}}$	Material waste ratio	–	0.1, found from the data used in Ruffo, Tuck, and Hague (2006)
${\rho }_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$	Density of material	$\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$	Find from the technical data of the used material
$P_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$	Porosity of material	–	Find from the technical data of the used material
$p_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$	Price of material	GBP/kg	Find from the material supplier's website
$R_{\mathrm{k}\mathrm{W}\mathrm{h}/\mathrm{k}\mathrm{g}}$	Consumption rate	kWh/kg	162.13, found from the data used in Brika et al. (2017)
$p_{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}$	Price of energy	GBP/kWh	Find from the energy supplier's website
$R_{\mathrm{G}\mathrm{B}\mathrm{P}/\mathrm{h}}$	Indirect cost rate	GBP/h	44.08, converted from 53.35 USD/h in Brika et al. (2017)
$T_{\mathrm{b}\mathrm{u}\mathrm{i}\mathrm{l}\mathrm{d}}^O$	Build time in O	h	Calculate using the estimation model in Equation (7(7) $T_{\mathrm{b}\mathrm{u}\mathrm{i}\mathrm{l}\mathrm{d}}^O=\frac{h_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}^O}{t_{\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}}}{T}_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}}+\frac{V_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}+V_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}}^O}{R_{\mathrm{b}\mathrm{u}\mathrm{i}\mathrm{l}\mathrm{d}}}$(7) )

Figure 5. Definition of the elements of a pairwise comparison matrix.

Table 3. The random index values when the matrix order is within 15.

n	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
RI	0.00	0.00	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49	1.51	1.54	1.56	1.57	1.59

Figure 6. The STL models of 12 LPBF parts.

Table 4. The basic information of the 12 LPBF parts.

Part Unit	Vertices –	Facets –	Surface –	Length mm	Width mm	Height mm	Area ${\mathrm{m}\mathrm{m}}^2$	Volume ${\mathrm{m}\mathrm{m}}^3$
Part 1	140	284	Regular	38.31	10.00	25.40	2629.50	2864.45
Part 2	410	828	Regular	27.00	16.00	23.00	2535.94	4593.24
Part 3	798	1592	Regular	120.00	80.00	167.89	60,941.50	404,405.00
Part 4	1181	2426	Regular	74.09	33.75	34.34	9137.33	9603.15
Part 5	1876	3776	Regular	125.00	75.00	80.00	46,576.40	228,889.00
Part 6	3160	6324	Regular	160.00	122.00	162.00	96,711.40	639,850.00
Part 7	6610	13,240	Freeform	35.89	26.48	22.04	2408.50	7354.99
Part 8	33,863	67,722	Freeform	119.81	88.13	94.90	36,451.00	535,216.00
Part 9	44,368	88,724	Freeform	86.06	56.88	68.00	17,165.80	88,637.20
Part 10	51,216	104,352	Freeform	34.05	33.88	60.00	5172.53	908.27
Part 11	54,314	108,888	Freeform	132.16	58.46	125.00	23,930.60	120,669.00
Part 12	80,276	161,606	Freeform	48.32	40.93	40.00	6915.89	1914.96

Table 5. The values of some variables for estimating factor values.

Variable Unit	$t_{\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}}$ mm	$T_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}}$ s	$s_{\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}}$ mm	$v_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}}$ mm/s	${\rho }_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$ kg/${\mathrm{m}}^3$	$P_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$ –	$p_{\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$ GBP/kg	$p_{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}$ GBP/kWh
Value	0.03	20	0.07	1,250	4,430	99.5%	247.86	0.16

Figure 7. Schematic diagram of the generated alternative orientations of Part 1.

Table 6. The estimated factor values in the alternative orientations of Part 1.

Generated alternative orientation	$V_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}}^{O_i}$	$E_{\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}}^{O_i}$	$R{a}^{O_i}$	$T_{\mathrm{b}\mathrm{u}\mathrm{i}\mathrm{l}\mathrm{d}}^{O_i}$	$C_{\mathrm{b}\mathrm{u}\mathrm{i}\mathrm{l}\mathrm{d}}^{O_i}$
Unit of the factor value	${\mathrm{m}\mathrm{m}}^3$	${\mathrm{m}\mathrm{m}}^3$	μm	h	GBP
$O_1=(+0.0000,+0.0000,-1.0000)$	218.6600	22.1375	10.4642	2.1781	100.0687
$O_2=(+0.0000,+0.0000,+1.0000)$	145.9500	22.1375	10.4642	2.1704	99.6339
$O_3=(-0.3420,-0.9397,+0.0000)$	1880.5100	24.8010	10.9248	5.6166	253.8252
$O_4=(+0.3420,+0.9397,+0.0000)$	2610.2700	23.8270	10.9248	5.6938	258.1897
$O_5=(+0.0000,+1.0000,+0.0000)$	2408.1200	25.0293	10.9584	5.0262	228.4960
$O_6=(+0.0000,-1.0000,+0.0000)$	1731.7600	25.2946	10.9584	4.9547	224.4509

Figure 8. The generated optimal orientation of each of the 12 LPBF parts.

Table 7. The estimated factor values in the optimal orientation of each of the 12 LPBF parts.

Part	Generated optimal orientation	$V_{\mathrm{s}\mathrm{u}\mathrm{p}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}}^{O_i}$	$E_{\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}}^{O_i}$	$R{a}^{O_i}$	$T_{\mathrm{b}\mathrm{u}\mathrm{i}\mathrm{l}\mathrm{d}}^{O_i}$	$C_{\mathrm{b}\mathrm{u}\mathrm{i}\mathrm{l}\mathrm{d}}^{O_i}$
–	Unit of the factor value	${\mathrm{m}\mathrm{m}}^3$	${\mathrm{m}\mathrm{m}}^3$	μm	h	GBP
Part 1	$O_2=(+0.0000,+0.0000,+1.0000)$	145.9500	22.1375	10.4642	2.1704	99.6339
Part 2	$O_2=(+1.0000,+0.0000,+0.0000)$	167.4100	21.4108	10.5592	3.4667	159.0793
Part 3	$O_2=(+0.0000,+0.0000,+1.0000)$	13,377.0000	551.7687	10.8011	75.3003	3,869.0913
Part 4	$O_1=(+0.0000,+1.0000,+0.0000)$	4587.1500	78.8480	10.6058	7.7516	360.3676
Part 5	$O_1=(+0.0000,+0.0000,-1.0000)$	13,022.0000	375.1246	10.2877	40.4139	2,099.8284
Part 6	$O_2=(+0.0000,+0.0000,-1.0000)$	39,032.0000	840.0294	10.6613	101.8394	5,382.5733
Part 7	$O_4=(-0.0007,+0.0001,+0.9999)$	1183.3700	22.8656	10.6987	4.9844	230.9516
Part 8	$O_9=(-0.9746,+0.1419,+0.1731)$	15,849.0000	347.5876	10.8183	79.2603	4,219.0663
Part 9	$O_{17}=(+0.0884,+0.1803,+0.9796)$	10,913.8000	164.3367	10.6973	23.2229	1,154.6889
Part 10	$O_8=(+0.1199,-0.9915,+0.0500)$	8317.5850	49.3868	10.6976	7.2288	330.7878
Part 11	$O_1=(+0.9802,-0.1916,-0.0503)$	24,248.0000	228.8950	10.9073	26.9175	1,377.2533
Part 12	$O_{15}=(+0.4968,+0.2169,+0.8403)$	10,813.0400	66.2267	10.8418	8.4612	389.7227

Table 8. The actual build orientation determination time of the proposed method.

The input STL model of LPBF part (.stl)	Part 1	Part 2	Part 3	Part 4	Part 5	Part 6
Number of facets in the STL model ($n^{\prime }$)	284	828	1592	2426	3776	6324
Number of the alternative orientations (m)	6	6	6	8	8	8
Time of alternative orientation generation (s)	0.0156	0.0625	0.1106	0.1597	0.2895	0.4538
Time of factor value estimation (s)	0.0984	0.2681	0.5140	1.0292	1.5887	2.6461
Time of optimal orientation determination (s)	0.0150	0.0150	0.0147	0.0156	0.0156	0.0156
Time of the entire part orientation process (s)	0.1290	0.3456	0.6393	1.2045	1.8938	3.1155
The input STL model of LPBF part (.stl)	Part 7	Part 8	Part 9	Part 10	Part 11	Part 12
Number of facets in the STL model ($n^{\prime }$)	13,240	67,722	88,724	104,352	108,888	161,606
Number of the alternative orientations (m)	24	24	24	24	24	24
Time of alternative orientation generation (s)	0.9607	5.9256	9.6683	10.2501	10.6240	18.1546
Time of factor value estimation (s)	16.5983	84.8202	110.7432	131.0347	135.5582	202.8251
Time of optimal orientation determination (s)	0.0315	0.0310	0.0312	0.0313	0.0315	0.0313
Time of the entire part orientation process (s)	17.5905	90.7768	120.4427	141.3161	146.2137	221.0110

Figure 9. Efficiency comparison result of the proposed method and an existing one-step method.

Figure 10. Efficiency comparison result of the proposed method and Zhang et al.'s method.

Ruffo, M., C. Tuck, and R. Hague. 2006. “Cost Estimation for Rapid Manufacturing-laser Sintering Production for Low to Medium Volumes.” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 220 (9): 1417–1427.

 Web of Science ®Google Scholar

Brika, S. E., Y. F. Zhao, M. Brochu, and J. Mezzetta. 2017. “Multi-Objective Build Orientation Optimisation for Powder Bed Fusion by Laser.” Journal of Manufacturing Science and Engineering 139 (11): 111011.

 Web of Science ®Google Scholar

Data availability

The STL files of the 12 LPBF parts and the implementation code of the proposed method have been deposited in the GitHub repository (https://github.com/YuchuChingQin/LPBFPartOrientation).