Determination of Barreling of Aluminum Solid Cylinders During Cold Upsetting Using Genetic Algorithm

Kanca, Erdogan; Eyercioglu, Omer; Gunen, Ali; Demir, Mehmet

doi:10.1590/S1517-707620190001.0621

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Articles • Matéria (Rio J.) 24 (1) • 2019 • https://doi.org/10.1590/S1517-707620190001.0621 copy

Determination of Barreling of Aluminum Solid Cylinders During Cold Upsetting Using Genetic Algorithm

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This study presents Genetic Programming models for the formulation of barreling of aluminum solid cylinders during cold upsetting based on experimental results. The maximum and minimum radii of the barreled cylinders having different aspect ratio (d/h= 0.5, 1.0 and 2.0) were measured for various frictional conditions (m=0.1-0.4). The change in radii with respect to height reduction showed different trends before and after folding, therefore, the corresponding reduction ratios of folding were also determined by using incremental upsetting. Genetic programming models were prepared using the experimental results with the input variables of the aspect ratio, the friction coefficient, and the reduction in height. The minimum and maximum barreling radii were formulated as output taking the folding into consideration. The performance of proposed GP models are quite satisfactory (R² = 0.908-0.998).

Keywords
Upset; forging; barreling; bulging; axisymmetric compression

Lubrication	Friction factor (m)
Palm oil	0.1
MoS₂	0.2
Graphite	0.3
Dry	0.4

Model	Code	Input variable	Range	Code	Output variable	Range
Folding	d0	d/h	0.5-2	D.V	hf/h	0.2-0.92
Folding	d1	m	0-0.4	D.V	hf/h	0.2-0.92
ΔR_min	d0	d/h	0.5-2	D.V	ΔRmin	0.065-4.087
	d1	m	0-0.4
	d2	hf/h	0.2-0.92
ΔR_max	d0	d/h	0.5-2	D.V	ΔRmax	0.017-0.916
	d1	m	0-0.4
	d2	hf/h	0.2-0.92

Code	Function Set
S1	+, -, *, /
S2	+, -, *, /, √
S3	+, -, *, /, √, e^x
S4	+, -, *, /,√, ln
S5	+, -, *, /, √, e^x, X², X³
S6	+, -, *, /, √, e^x, ln, X², X³

P2	P3	P4			R² Error				R² Error
P2	P3	P4	P1	P5	Training	Test	P1	P5	Training	Test
1	7		S1	12982	0.999	0.998	S4	10918	0.978	0.967
2	8	+	S1	13876	0.989	0.971	S4	14763	0.989	0.956
2	8	*	S1	17987	0.992	0.991	S4	12835	0.978	0.965
1	7		S2	10982	0.937	0.912	S5	12982	0.919	0.927
2	8	+	S2	19276	0.945	0.938	S5	11022	0.978	0.987
2	8	*	S2	11287	0.992	0.987	S5	12023	0.996	0.991
1	7		S3	10987	0.918	0.901	S6	17934	0.987	0.991
2	8	+	S3	10234	0.902	0.918	S6	12922	0.992	0.990
2	8	*	S3	12897	0.992	0.989	S6	17823	0.987	0.919

				R² Error
P1	P2	P3	P4	Before Folding			After Folding
P1	P2	P3	P4	P5	Training	Test	P5	Training	Test
S1	1	7		12789	0.972	0.961	11092	0.881	0.941
S1	2	8	+	10987	0.957	0.920	12928	0.925	0.798
S1	2	8	*	10098	0.952	0.966	13098	0.882	0.918
S1	3	10	+	17345	0.946	0.956	12098	0.931	0.752
S1	3	10	*	12674	0.961	0.957	17646	0.927	0.795
S2	1	7		15897	0.868	0.895	13756	0.885	0.948
S2	2	8	+	13980	0.927	0.929	12345	0.902	0.867
S2	2	8	*	12453	0.918	0.891	12876	0.916	0.800
S2	3	10	+	14098	0.927	0.952	14908	0.904	0.890
S2	3	10	*	17908	0.976	0.944	15093	0.925	0.765
S3	1	7		19037	0.874	0.912	10289	0.889	0.930
S3	2	8	+	18905	0.919	0.916	17893	0.931	0.842
S3	2	8	*	17457	0.950	0.962	13098	0.902	0.848
S3	3	10	+	14098	0.953	0.933	14678	0.913	0.853
S3	3	10	*	12098	0.952	0.911	16782	0.916	0.824
S4	1	7		10982	0.928	0.947	17829	0.929	0.910
S4	2	8	+	11902	0.937	0.885	17294	0.917	0.804
S4	2	8	*	12098	0.969	0.959	19038	0.892	0.905
S4	3	10	+	10928	0.944	0.948	18990	0.936	0.741
S4	3	10	*	11098	0.974	0.945	12782	0.935	0.762
S5	1	7		12346	0.837	0.889	18296	0.888	0.914
S5	2	8	+	11093	0.952	0.953	12983	0.909	0.900
S5	2	8	*	19022	0.951	0.961	13739	0.904	0.857
S5	3	10	+	18902	0.939	0.964	11902	0.948	0.774
S5	3	10	*	19025	0.956	0.965	11386	0.934	0.807
S6	1	7		12987	0.819	0.897	11091	0.890	0.904
S6	2	8	+	11238	0.937	0.938	10982	0.922	0.755
S6	2	8	*	12092	0.974	0.951	18296	0.913	0.879
S6	3	10	+	11092	0.938	0.935	17298	0.930	0.840
S6	3	10	*	19029	0.960	0.961	12987	0.922	0.869

				R² Error
P1	P2	P3	P4	Before Folding			After Folding
P1	P2	P3	P4	P5	Training	Test	P5	Training	Test
S1	1	7		18724	0.735	0.734	19028	0.831	0.727
S1	2	8	+	18414	0.903	0.870	18290	0.887	0.615
S1	2	8	*	10552	0.934	0.916	10234	0.896	0.665
S1	3	10	+	11913	0.961	0.951	11098	0.931	0.813
S1	3	10	*	19366	0.950	0.934	10926	0.899	0.907
S2	1	7		19742	0.795	0.848	10922	0.759	0.543
S2	2	8	+	17399	0.933	0.928	11098	0.868	0.637
S2	2	8	*	15283	0.909	0.904	12456	0.618	0.747
S2	3	10	+	14567	0.905	0.894	18654	0.899	0.824
S2	3	10	*	14154	0.964	0.960	19546	0.898	0.764
S3	1	7		13700	0.744	0.696	17546	0.826	0.474
S3	2	8	+	13717	0.861	0.886	13893	0.895	0.735
S3	2	8	*	17565	0.822	0.825	19296	0.881	0.805
S3	3	10	+	19127	0.815	0.848	10289	0.943	0.873
S3	3	10	*	18178	0.888	0.849	14628	0.908	0.751
S4	1	7		19174	0.689	0.802	18021	0.772	0.703
S4	2	8	+	18216	0.900	0.877	10012	0.901	0.720
S4	2	8	*	15219	0.909	0.906	19012	0.910	0.901
S4	3	10	+	17620	0.918	0.906	19037	0.930	0.861
S4	3	10	*	17720	0.907	0.887	16345	0.908	0.745
S5	1	7		15404	0.824	0.863	13752	0.735	0.632
S5	2	8	+	19789	0.888	0.882	12903	0.844	0.561
S5	2	8	*	17591	0.893	0.878	19820	0.904	0.861
S5	3	10	+	18601	0.946	0.925	12903	0.904	0.881
S5	3	10	*	19603	0.959	0.974	11098	0.940	0.838
S6	1	7		18655	0.774	0.799	10283	0.737	0.815
S6	2	8	+	17264	0.894	0.874	11902	0.910	0.816
S6	2	8	*	18033	0.907	0.917	16830	8.892	0.844
S6	3	10	+	18858	0.942	0.922	18936	0.904	0.759
S6	3	10	*	17536	0.934	0.951	12903	0.874	0.922

			ΔR_min				ΔR_max
	Folding Point		Before Folding		After Folding		Before Folding		After Folding
	Train	Test	Train	Test	Train	Test	Train	Test	Train	Test
MSE	0,0003	0,0005	0,061	0,045	0,045	0,037	0,003	0,003	0,006	0,008
MAE	0,0160	0,0205	0,172	0,158	0,165	0,172	0,044	0,046	0,071	0,073
R	0,9995	0,9889	0,971	0,980	0,943	0,964	0,966	0,963	0,911	0,902

				R_min		R_min(T/GP)	R_max		R_max(T/GP)
No:	m	d/h	hf/h	Test	GP	R_min(T/GP)	Test	GP	R_max(T/GP)
1	0,1	0,5	0,84	13,48	13,50	0,9985	13,66	13,71	0,9961
2	0,1	0,5	0,76	14,08	14,12	0,9967	14,39	14,45	0,9962
3	0,1	0,5	0,68	14,77	14,85	0,9945	15,26	15,30	0,9972
4	0,1	0,5	0,6	15,60	15,72	0,9921	16,28	16,30	0,9989
5	0,1	0,5	0,52	16,62	16,79	0,9898	17,51	17,50	1,0005
6	0,1	0,5	0,44	17,90	18,13	0,9869	19,04	19,01	1,0014
7	0,1	0,5	0,2	26,52	26,49	1,0010	27,96	28,02	0,9981
8	0,2	0,5	0,92	12,87	12,90	0,9975	13,06	13,04	1,0015
9	0,2	0,5	0,76	13,87	13,91	0,9975	14,44	14,52	0,9948
10	0,2	0,5	0,68	14,46	14,55	0,9942	15,34	15,40	0,9966
11	0,2	0,5	0,6	15,16	15,31	0,9901	16,40	16,41	0,9994
12	0,2	0,5	0,52	15,99	16,25	0,9842	17,67	17,63	1,0020
13	0,2	0,5	0,44	16,96	17,43	0,9733	19,20	19,14	1,0031
14	0,2	0,5	0,28	22,12	22,00	1,0053	23,92	23,83	1,0036
15	0,3	0,5	0,92	12,81	12,84	0,9977	13,08	13,00	1,0056
16	0,3	0,5	0,76	13,69	13,69	1,0001	14,48	14,56	0,9942
17	0,3	0,5	0,68	14,19	14,24	0,9966	15,40	15,47	0,9956
18	0,3	0,5	0,6	14,76	14,90	0,9908	16,49	16,51	0,9987
19	0,3	0,5	0,52	15,39	15,70	0,9803	17,76	17,73	1,0013
20	0,3	0,5	0,44	17,06	16,94	1,0067	19,30	19,26	1,0020
21	0,3	0,5	0,28	21,85	21,87	0,9994	24,03	23,94	1,0036
22	0,3	0,5	0,2	26,36	26,27	1,0034	28,18	28,14	1,0014
23	0,4	0,5	0,92	12,76	12,77	0,9986	13,09	12,96	1,0102
24	0,4	0,5	0,84	13,14	13,10	1,0031	13,72	13,75	0,9978
25	0,4	0,5	0,76	13,53	13,48	1,0040	14,50	14,60	0,9934
26	0,4	0,5	0,68	13,95	13,93	1,0011	15,44	15,54	0,9938
27	0,4	0,5	0,52	15,42	15,19	1,0157	17,82	17,76	1,0032
28	0,4	0,5	0,44	16,42	16,76	0,9793	19,38	19,40	0,9986
29	0,4	0,5	0,36	18,50	18,82	0,9831	21,37	21,37	0,9999
30	0,4	0,5	0,2	26,37	26,07	1,0114	28,23	28,21	1,0007
31	0,1	1	0,92	25,91	25,98	0,9973	26,14	26,12	1,0009
32	0,1	1	0,76	28,28	28,40	0,9957	28,82	28,81	1,0003
33	0,1	1	0,68	29,76	29,92	0,9947	30,50	30,48	1,0006
34	0,1	1	0,6	31,54	31,74	0,9936	32,49	32,46	1,0010
35	0,1	1	0,44	36,39	36,77	0,9897	37,95	37,88	1,0016
36	0,1	1	0,36	39,84	40,46	0,9848	41,89	41,85	1,0008
37	0,1	1	0,2	53,83	53,94	0,9980	55,70	55,96	0,9955
38	0,2	1	0,92	25,78	25,90	0,9956	26,21	26,17	1,0015
39	0,2	1	0,84	26,78	26,93	0,9946	27,49	27,48	1,0005
40	0,2	1	0,76	27,93	28,12	0,9932	28,97	28,95	1,0006
41	0,2	1	0,6	30,86	31,21	0,9887	32,72	32,65	1,0022
42	0,2	1	0,44	35,37	35,85	0,9866	38,19	38,08	1,0029
43	0,2	1	0,28	45,08	45,12	0,9990	47,54	47,46	1,0017
44	0,2	1	0,2	53,71	53,86	0,9974	55,85	56,01	0,9971
45	0,3	1	0,92	25,66	25,81	0,9942	26,28	26,22	1,0020
46	0,3	1	0,76	27,59	27,84	0,9909	29,10	29,09	1,0005
47	0,3	1	0,68	28,77	29,13	0,9877	30,86	30,82	1,0013
48	0,3	1	0,6	30,13	30,67	0,9823	32,90	32,83	1,0021
49	0,3	1	0,44	35,19	35,29	0,9973	38,38	38,30	1,0023
50	0,3	1	0,28	45,10	44,99	1,0025	47,68	47,56	1,0026
51	0,3	1	0,2	53,86	53,72	1,0027	55,97	56,06	0,9984
52	0,4	1	0,92	25,57	25,73	0,9938	26,32	26,28	1,0015
53	0,4	1	0,76	27,28	27,56	0,9897	29,20	29,23	0,9990
54	0,4	1	0,68	28,30	28,73	0,9848	30,97	30,98	0,9995
55	0,4	1	0,6	30,00	30,14	0,9953	33,02	33,02	0,9999
56	0,4	1	0,52	31,83	32,02	0,9942	35,47	35,59	0,9967
57	0,4	1	0,44	34,96	35,11	0,9958	38,49	38,50	0,9998
58	0,4	1	0,36	38,91	39,15	0,9939	42,37	42,30	1,0018
59	0,4	1	0,28	44,94	44,80	1,0030	47,72	47,67	1,0011
60	0,1	2	0,92	51,99	52,01	0,9996	52,18	52,19	0,9998
61	0,1	2	0,84	54,27	54,30	0,9995	54,64	54,66	0,9997
62	0,1	2	0,76	56,91	56,95	0,9994	57,48	57,50	0,9996
63	0,1	2	0,6	63,71	63,77	0,9991	64,72	64,74	0,9997
64	0,1	2	0,52	68,23	68,32	0,9988	69,51	69,54	0,9996
65	0,1	2	0,44	73,89	74,04	0,9980	75,52	75,58	0,9992
66	0,1	2	0,28	91,93	92,09	0,9982	94,31	94,66	0,9963
67	0,1	2	0,2	108,85	108,84	1,0001	111,06	111,82	0,9932
68	0,2	2	0,92	51,87	51,89	0,9996	52,24	52,26	0,9996
69	0,2	2	0,84	54,02	54,04	0,9996	54,76	54,78	0,9996
70	0,2	2	0,76	56,53	56,54	0,9998	57,64	57,65	0,9998
71	0,2	2	0,6	62,99	63,00	0,9998	64,98	64,95	1,0005
72	0,2	2	0,52	67,23	67,29	0,9990	69,80	69,75	1,0006
73	0,2	2	0,44	72,46	72,71	0,9966	75,81	75,79	1,0003
74	0,2	2	0,28	91,51	91,37	1,0015	94,51	94,62	0,9988
75	0,2	2	0,2	108,96	108,76	1,0019	111,12	111,84	0,9936
76	0,3	2	0,92	51,74	51,76	0,9996	52,29	52,34	0,9992
77	0,3	2	0,76	56,14	56,14	1,0001	57,79	57,81	0,9996
78	0,3	2	0,68	58,92	58,91	1,0002	61,18	61,18	1,0000
79	0,3	2	0,52	66,09	66,27	0,9973	70,00	69,97	1,0003
80	0,3	2	0,36	80,61	80,00	1,0076	83,78	83,70	1,0009
81	0,3	2	0,28	91,43	91,23	1,0022	94,58	94,69	0,9988
82	0,3	2	0,2	108,61	108,62	0,9999	111,13	111,86	0,9935
83	0,4	2	0,92	51,62	51,64	0,9996	52,35	52,41	0,9987
84	0,4	2	0,84	53,52	53,53	0,9997	54,96	55,02	0,9988
85	0,4	2	0,76	55,74	55,73	1,0000	57,92	57,98	0,9991
86	0,4	2	0,68	58,32	58,33	0,9998	61,34	61,37	0,9995
87	0,4	2	0,52	66,05	65,25	1,0122	70,15	70,19	0,9995
88	0,4	2	0,44	71,83	71,80	1,0005	76,13	76,11	1,0003
89	0,4	2	0,36	79,66	79,82	0,9980	83,88	83,82	1,0007
90	0,4	2	0,28	90,53	91,04	0,9943	94,61	94,75	0,9985

Laboratório de Hidrogênio, Coppe - Universidade Federal do Rio de Janeiro, em cooperação com a Associação Brasileira do Hidrogênio, ABH2 Av. Moniz Aragão, 207, 21941-594, Rio de Janeiro, RJ, Brasil, Tel: +55 (21) 3938-8791 - Rio de Janeiro - RJ - Brazil
E-mail: revmateria@gmail.com

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[1] e-mail: erdogan.kanca@iste.edu.tr; Mehmet.demir@iste.edu.tr, ali.gunen@iste.edu.tr, omer.eyercioglu@gantep.edu.tr

P1	Function Set	+, -, *, /, V, ex, ln, log, tan, X², X³
P2	Number of Genes	1,2,3,4,5,6
P3	Head Size	3, 5, 8, 10, 12, 15
P4	Linking Function	Addition (+), Multiplication (*)
P5	Number of Generation	10000 and 20000
P6	Chromosomes	30-45
P7	Mutation Rate	0.044
P8	Inversion Rate	0.1
P9	One-point Recombination Rate	0.3
P10	Two-point Recombination Rate	0.1
P11	Gene Recombination Rate	0.1
P12	Gene transposition Rate	0,1