Simulation and multi-objective optimization to improve the final shape and process efficiency of a laser-based material accumulation process

Bänsch, Eberhard; Luttmann, Andreas; Montalvo-Urquizo, Jonathan; Schmidt, Alfred; Villarreal-Marroquín, Maria G.

doi:10.1186/s13362-020-0070-y

Journal of Mathematics in Industry

Table 5 Case Study 2: Evaluation of selected predicted Pareto solutions. Iterations are divided by horizontal lines. Iteration 1: solutions 16 to 33, Iteration 2: 33 to 51, Iteration 3: 52 to 69

From: Simulation and multi-objective optimization to improve the final shape and process efficiency of a laser-based material accumulation process

Run	P	s	v	Δl	\(\Delta c_{xy}\)	\(\Delta c_{z}\)	Process	E	Laser usage
Run	[W]	[mm]	[mm/s]	[mm]	[μm]	[μm]	time [ms]	[J]	[ms]
16	35.35	2.51	33.99	−0.1259	18.9614	6.2589	311.76	2.61	73.70
17	49.90	2.18	33.99	0.0822	24.8656	10.8807	344.71	3.20	64.19
18^∗	49.90	2.54	52.25	−0.2156	5.6817	0.8054	290.20	2.42	48.53
19^∗	53.13	2.37	46.77	−0.1091	25.1997	2.4081	307.57	2.70	50.75
20^∗	53.94	2.97	85.11	−1.6574	0.4341	478.3233	105.03	1.88	34.89
21^∗	54.75	2.63	66.85	−0.3791	44.9556	5.0348	256.53	2.15	39.29
22^∗	63.64	2.60	77.81	−0.3833	24.5226	3.5034	253.24	2.12	33.36
23^∗	65.25	2.62	85.11	−0.4678	33.2967	5.0032	230.85	2.01	30.74
24^∗	66.06	2.23	52.25	−0.0218	1.4280	12.3484	319.60	2.82	42.73
25^∗	66.06	2.26	65.03	−0.3948	7.2521	1.1002	280.10	2.30	34.79
26^∗	74.14	2.34	81.46	−0.4587	38.3614	0.9513	252.87	2.13	28.77
27^∗	78.99	2.88	90.59	0.0049	26.3575	4.2562	293.01	2.51	31.78
28^∗	87.07	2.24	86.94	−0.4137	1.4837	2.2683	268.51	2.25	25.79
29	87.07	2.68	117.97	−0.4491	53.1142	9.8716	226.00	1.98	22.69
30^∗	89.50	2.82	96.06	0.1170	12.5026	4.3378	300.99	2.63	29.34
31^∗	93.54	2.93	159.97	−2.2449	0.2254	227.3149	67.02	1.71	18.31
32^∗	98.38	2.45	105.19	−0.3005	0.2400	3.9460	268.81	2.30	23.33
33^∗	100.00	2.66	96.06	0.2074	24.5266	1.4533	322.17	2.77	27.65
34	29.70	2.99	24.86	0.5677	32.4914	1.8269	408.92	3.57	120.27
35^∗	43.43	2.97	48.59	0.1526	3.6120	4.8132	311.67	2.65	61.11
36^∗	48.28	2.95	59.55	−0.0506	35.7041	6.3111	283.81	2.39	49.53
37^∗	57.17	2.85	65.03	−0.0030	25.9235	2.2283	289.99	2.50	43.81
38^∗	63.64	2.89	79.63	−0.1301	31.8396	1.6049	270.27	2.31	36.28
39	69.29	2.24	50.42	0.1363	21.4663	4.6353	321.10	3.08	44.47
40^∗	70.10	2.84	88.76	−0.1998	0.9327	2.7809	261.26	2.24	31.98
41	70.10	2.97	72.33	0.3310	19.4154	3.7056	327.64	2.88	41.06
42^∗	78.99	2.57	99.72	−0.4796	12.5994	3.9512	237.23	2.03	25.73
43	79.80	2.31	55.90	0.3092	19.1094	7.3058	343.88	3.30	41.38
44^∗	80.61	2.85	130.75	−1.8735	0.1271	381.8099	75.81	1.76	21.79
45	81.41	2.16	46.77	0.4455	0.6707	3.0974	358.19	3.76	46.22
46^∗	85.45	2.53	72.33	0.2835	0.3908	1.6543	340.41	2.98	34.91
47^∗	85.45	2.88	139.88	−1.9057	0.2091	367.6946	71.80	1.76	20.58
48^∗	93.54	2.57	107.02	−0.3093	48.1271	1.2762	263.48	2.24	23.97
49^∗	95.15	2.06	52.25	0.3811	15.2397	0.2559	346.68	3.75	39.44
50^∗	99.19	2.91	139.88	−0.2351	74.7555	11.2608	215.66	2.06	20.80
51^∗	99.19	2.95	127.10	−0.1003	12.5657	4.7182	259.21	2.30	23.21
52	28.08	2.02	10.25	−0.3540	2.8358	2.4017	405.85	5.53	197.02
53^∗	48.28	2.94	74.16	−0.9304	1.8047	886.3475	145.87	1.91	39.64
54^∗	53.13	2.95	77.81	−0.2435	99.7576	25.4293	202.43	2.01	37.91
55^∗	74.95	2.79	110.67	−0.4035	101.1778	20.9598	184.90	1.89	25.19
56^∗	79.80	2.84	125.28	−1.1145	2.3559	716.2545	83.38	1.81	22.66
57^∗	84.65	2.95	119.80	−0.2084	85.2085	25.9385	207.79	2.08	24.62
58^∗	85.46	2.97	136.23	−1.5395	0.3145	524.8515	78.70	1.86	21.80
59^∗	86.26	2.71	125.28	−0.4241	79.7294	19.6772	184.75	1.86	21.61
60^∗	87.07	2.01	55.90	0.0949	21.1008	5.4781	333.35	3.13	35.96
61^∗	88.69	2.63	116.15	−0.4445	30.6019	5.3633	235.61	2.01	22.61
62^∗	91.11	2.92	136.23	−0.2447	48.5104	0.9139	193.50	1.95	21.43
63	92.73	2.99	119.80	−0.1034	55.0695	10.4963	263.55	2.31	24.96
64^∗	93.54	3.00	149.01	−1.4214	0.5304	577.4269	82.75	1.88	20.13
65^∗	94.34	2.91	128.93	−0.2180	78.6193	14.0482	218.64	2.13	22.56
66	95.96	2.26	101.54	−0.4763	9.4468	5.5457	262.71	2.14	22.28
67^∗	100.00	2.12	81.46	−0.1803	4.3243	3.2005	296.08	2.60	26.04
68^∗	100.00	2.69	130.75	−0.3969	4.7074	4.3802	236.32	2.05	20.55
69^∗	100.00	2.89	165.44	−1.9310	0.2932	358.7323	61.29	1.75	17.46

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