Optimization of duplex stainless steel UNS S32205 end milling with noise factor analysisy

Ribeiro, Wander Pinto; Oliveira, Carlos Henrique de; Oliveira, Leonardo Albergaria; Brito, Tarcísio Gonçalves de; Paiva, Emerson José de; Peruchi, Rogério Santana

doi:10.1590/0370-44672023770119

Wander Pinto Ribeiro ³ 3 wander.p.ribeiro@gmail.com

Universidade Federal de Itajubá- UNIFEI, Instituto de Engenharias Integradas, Departamento de Engenharia Mecânica, Itabira - Minas Gerais -Brasil

https://orcid.org/0000-0003-1757-7589

Carlos Henrique de Oliveira ⁴ 4 carlos.henrique@unifei.edu.br

Universidade Federal de Itajubá- UNIFEI, Instituto de Engenharias Integradas, Departamento de Engenharia Mecânica, Itabira - Minas Gerais -Brasil

https://orcid.org/0000-0001-8406-5255

Leonardo Albergaria Oliveira ⁵ 5 leoalber@unifei.edu.br

Universidade Federal de Itajubá- UNIFEI, Instituto de Engenharias Integradas, Departamento de Engenharia Mecânica, Itabira - Minas Gerais -Brasil

https://orcid.org/0000-0001-8810-4987

Tarcísio Gonçalves de Brito ⁶ 6 tgbrito@unifei.edu.br

Universidade Federal de Itajubá- UNIFEI, Instituto de Engenharias Integradas, Departamento de Engenharia Mecânica, Itabira - Minas Gerais -Brasil

https://orcid.org/0000-0001-6364-2359

Emerson José de Paiva ⁷ 7 emersonpaiva@unifei.edu.br

Universidade Federal de Itajubá- UNIFEI, Instituto de Engenharias Integradas, Departamento de Engenharia Mecânica, Itabira - Minas Gerais -Brasil

https://orcid.org/0000-0001-5266-1183

Rogério Santana Peruchi ⁸ 8 rsp@academ ico.ufpb.br

Universidade Federal da Paraíba - UFPB, Departamento de Engenharia de Produção, João Pessoa - Paraíba - Brasil

https://orcid.org/0000-0002-0436-9214

3 wander.p.ribeiro@gmail.com

4 carlos.henrique@unifei.edu.br

5 leoalber@unifei.edu.br

6 tgbrito@unifei.edu.br

7 emersonpaiva@unifei.edu.br

8 rsp@academ ico.ufpb.br

Variables	Levels
Variables	-2.83	-1	0	1	2.83
Cutting Speed (v_c) [m/min]	32.50	60.00	75.00	90.00	117.40
Feed per tooth (f_z) [mm/tooth]	0.04	0.10	0.13	0.16	0.21
Radial depth of cut (a_e) [mm]	12.26	15.00	16.50	18.00	20.74
Axial depth of cut (a_p) [mm]	0.43	0.80	1.00	1.20	1.57

Variables	Levels
Variables	-1	0	1
Flank wear (y_b) [mm]	0	0.15	0.30
Fluid flow rate (Q) [l/min].	0	10	20
Fluid concentration (C) [%]	0	10	20

C	Si	Mn	Ρ	S	Ν	AI	Cr	Mo	Ni	Cu	W	Co
0.01	0.47	1.22	0.019	0.01	0.19	0.00	22.2	3.14	5.62	0.19	0.02	0.05

Experiments	Control Variables				Noise Variables			Answers
Experiments	V_c	f_z	a_e	a_p	v_b	Q	C	R_a	R_t
1	-1	-1	-1	-1	-1	-1	1	0.520	4.210
2	1	-1	-1	-1	-1	-1	-1	0.347	2.760
3	-1	1	-1	-1	-1	-1	-1	0.630	3.667
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
80	0	0	0	0	0	0	0	0.380	2.837
81	0	0	0	0	0	0	0	0.340	2.640
82	0	0	0	0	0	0	0	0.397	3.136

R_a					R_t
Term	Coef	EP of Coef	T-value	P-value	Term	Coef	EP of Coef	T-value	P-value
Constant	0.42560	0.01350	31.54	0.000	Constant	3.04570	0.0942	32.32	0.000
ν_c	0.01597	0.00591	2.70	0.009	ν_c	0.03850	0.0413	0.93	0.355
f_z	0.05574	0.00591	9.43	0.000	f_z	0.29390	0.0413	7.12	0.000
a_e	0.00198	0.00591	0.34	0.738	a_e	-0.02150	0.0413	-0.52	0.605
a_p	0.00826	0.00591	1.40	0.168	a_p	0.12340	0.0413	2.99	0.004
v_b	0.13823	0.00661	20.93	0.000	v_b	0.71500	0.0461	15.50	0.000
Q	-0.05342	0.00661	-8.09	0.000	Q	-0.10670	0.0461	-2.31	0.025
C	0.00452	0.00661	0.68	0.497	C	-0.08610	0.0461	-1.87	0.068
V_c × V_c	0.04525	0.00511	8.86	0.000	V_c × V_c	0.29020	0.0357	8.14	0.000
V_z × V_z	0.06038	0.00511	11.82	0.000	V_z × V_z	0.38380	0.0357	10.76	0.000
a_e × a_e	0.06725	0.00511	13.17	0.000	a_e × a_e	0.32590	0.0357	9.14	0.000
a_p × a_p	0.04563	0.00511	8.93	0.000	a_p × a_p	0.26140	0.0357	7.33	0.000
V_c × f_z	0.08814	0.00661	13.34	0.000	V_c × f_z	0.49540	0.0461	10.74	0.000
V_c × a_e	-0.00517	0.00661	-0.78	0.437	V_c × a_e	-0.06880	0.0461	-1.49	0.142
V_c × a_p	-0.01127	0.00661	-1.71	0.094	V_c × a_p	-0.02750	0.0461	-0.60	0.554
*V_c × V_b*	0.03502	0.00661	5.30	0.000	*V_c × V_b*	0.27490	0.0461	5.96	0.000
V_c × Q	0.00005	0.00661	0.01	0.994	V_c × Q	0.00090	0.0461	0.02	0.985
V_c × C	0.00117	0.00661	0.18	0.860	V_c × C	-0.05270	0.0461	-1.14	0.259
f_z × a_e	0.00542	0.00661	0.82	0.415	f_z × a_e	-0.02190	0.0461	-0.48	0.636
f_z × a_b	0.01033	0.00661	1.56	0.124	f_z × a_b	0.08670	0.0461	1.88	0.066
*f_z × v_b*	-0.07577	0.00661	-11.47	0.000	*f_z × v_b*	-0.29080	0.0461	-6.30	0.000
f_z × Q	-0.00805	0.00661	-1.22	0.229	f_z × Q	0.12220	0.0461	2.65	0.011
f_z × C	0.00295	0.00661	0.45	0.657	f_z × C	0.00690	0.0461	0.15	0.882
a_e × a_b	-0.00548	0.00661	-0.83	0.410	a_e × a_b	0.04770	0.0461	1.04	0.305
a_e × v_b	0.00492	0.00661	0.75	0.460	*a_e × v_b*	0.11580	0.0461	2.51	0.015
a_e × Q	-0.00173	0.00661	-0.26	0.794	a_e × Q	-0.00470	0.0461	-0.10	0.918
a_e × C	-0.00555	0.00661	-0.84	0.405	a_e × C	-0.02480	0.0461	-0.54	0.593
a_p × vb	0.01014	0.00661	1.54	0.131	*a_p × vb*	0.12050	0.0461	2.61	0.012
a_b × Q	0.00392	0.00661	0.59	0.555	a_b × Q	0.00540	0.0461	0.12	0.908
a_b × C	-0.00545	0.00661	-0.83	0.413	a_b × Q	-0.06470	0.0461	-1.40	0.167
S	R²	R²(adj.)	R²(pred)		S	R²	R²(adj.)	R²(pred)
0.052841	96.09%	93.91%	89.93%		0.369048	93.51%	89.89%	83.30%

Weight w₁	Weight w₂	V_c (m/min)	f_z (mm/tooth)	a_e (mm)	a_p (mm)	μ (R_a) (pm)	μ (R_t) (μm)	EQM R_a	EQM R_t
0.00	1.00	61.27	0.15	16.30	0.90	0.4529273	3.2568946	0.0127131	0.2872047
0.05	0.95	61.27	0.15	16.30	0.90	0.4529343	3.2570000	0.0127102	0.2872048
0.10	0.90	61.26	0.15	16.30	0.90	0.4529421	3.2571168	0.0127069	0.2872051
0.15	0.85	61.26	0.15	16.30	0.90	0.4529508	3.2572470	0.0127032	0.2872056
0.20	0.80	61.25	0.15	16.30	0.90	0.4529606	3.2573932	0.0126992	0.2872065
0.25	0.75	61.24	0.15	16.30	0.90	0.4529717	3.2575584	0.0126946	0.2872078
0.30	0.70	61.23	0.15	16.30	0.90	0.4529844	3.2577465	0.0126894	0.2872098
0.35	0.65	61.22	0.15	16.30	0.90	0.4529990	3.2579628	0.0126835	0.2872126
0.40	0.60	61.21	0.15	16.30	0.90	0.4530161	3.2582140	0.0126766	0.2872168
0.45	0.55	61.20	0.15	16.30	0.90	0.4530362	3.2585092	0.0126687	0.2872227
0.50	0.50	61.18	0.15	16.30	0.90	0.4530603	3.2588614	0.0126592	0.2872312
0.55	0.45	61.16	0.15	16.30	0.90	0.4530897	3.2592885	0.0126480	0.2872437
0.60	0.40	61.13	0.15	16.30	0.90	0.4531263	3.2598175	0.0126342	0.2872625
0.65	0.35	61.10	0.15	16.30	0.90	0.4531733	3.2604895	0.0126170	0.2872913
0.70	0.30	61.06	0.15	16.30	0.90	0.4532355	3.2613718	0.0125950	0.2873374
0.75	0.25	61.00	0.15	16.30	0.90	0.4533220	3.2625809	0.0125657	0.2874153
0.80	0.20	60.92	0.15	16.30	0.90	0.4534499	3.2643394	0.0125250	0.2875578
0.85	0.15	60.79	0.15	16.31	0.90	0.4536578	3.2671304	0.0124642	0.2878501
0.90	0.10	60.57	0.15	16.31	0.90	0.4540517	3.2722345	0.0123644	0.2885748
0.95	0.05	60.05	0.15	16.31	0.91	0.4550575	3.2845232	0.0121720	0.2911673
1.00	0.00	57.36	0.15	16.30	0.93	0.4615971	3.3549912	0.0117800	0.3216968

Control Variables					μ (R_a)	μ (R_t)	σ²(R_a)	σ²(R_t)
	V_c	f_z	a_e	a_p
Optimum values	60.79	0.1881	16.31	0.90	0.4534	3.2671	0.0095	0.1821
Unit	m/min	mm/tooth	Mm	Mm	μm	μm	μm²	μm²

v_b	Q	C	R_a (Real)	R_t (Real)
0.00	0	0	0.431	3.544
0.00	10	10	0.427	3.386
0.00	20	20	0.474	3.281
0.15	0	10	0.456	3.238
0.15	10	20	0.441	3.470
0.15	20	0	0.482	3.577
0.30	0	20	0.451	3.310
0.30	10	0	0.470	3.518
0.30	20	10	0.513	3.265
	Average (real)		0.461	3.399
	Expected Value		0.454	3.267
	Error		1.51%	3.87%

Source	GL	SQ(Aj.)	QM(Aj.)	F-Value	P-Value
V_b	2	0.001738	0.000869	6.38	0.13500
Q	2	0.003814	0.001907	14.01	0.06700
C	2	0.000151	0.000075	0.55	0.64300
Error	2	0.000272	0.000136
Total	8	0.005974

Source	GL	SQ(Aj.)	QM(Aj.)	F-Value	P-Value
V_b	2	0.006288	0.003144	0.50	0.66800
Q	2	0.015961	0.007980	1.26	0.44200
C	2	0.102976	0.051488	8.13	0.10900
Error	2	0.012659	0.006329
Total	8	0.137883

y (x, z) = β_{0} + \sum_{i = 1}^{k} β_{i} x_{i} + \sum_{i = 1}^{k} β_{i i} x^{2}_{i} + \sum_{i < j} \sum β_{i j} x_{i} x_{j} + \sum_{i = 1}^{r} y_{i} z_{i} + \sum_{i - 1}^{k} \sum_{j = 1}^{r} δ_{i j} x_{i} z_{j} + ε

R_{a}, R_{t} (x, z) = β_{0} + β_{1} f_{z} + β_{2} a_{p} + β_{3} v_{c} + β_{4} a_{e} + β_{11} f_{z}^{2} + β_{22} a_{P}^{2} + β_{33} v_{c}^{2} + β_{44} a_{e}^{2} + β_{12} f_{z} a_{p} + β_{13} f_{z} v_{c} + β_{14} f_{z} a_{e} + β_{23} a_{p} v_{c} + β_{24} a_{p} a_{e} + β_{34} v_{c} a_{e} + γ_{1} v_{b} + γ_{2} C + γ_{3} Q + δ 11 f_{z} v_{b} + δ_{12} f_{z} C + δ_{13} f_{z} Q + δ_{21} a_{p} v_{b} + δ_{22} a_{p} + δ_{23} a_{p} Q + δ_{31} v_{c} v_{b} + δ_{32} v_{c} C + δ_{33} v_{c} Q + δ_{41} a_{e} v_{b} + δ_{42} a_{e} C + δ_{43} a_{e} Q

\begin{array}{l} R_{a} (x, z) = 0.4256 + 0.01597 v_{c} + 0.05574 f_{z} - 0.00198 a_{e} + 0.00826 a_{p} + 0.13823 v_{b} \\ - 0.05342 Q + 0.00452 C + 0.04525 v_{c}^{2} + 0.06038 f_{z}^{2} + 0.0672 a_{e}^{2} \\ + 0.04563 a_{p}^{2} + 0.08814 v_{c} f_{z} - 0.00517 v_{c} a_{e} - 0.01127 v_{c} a_{p} \\ + 0.03502 v_{c} v_{b} + 0.00005 v_{c} Q + 0.00117 v_{c} C + 0.00542 f_{z} a_{e} \\ + 0.01033 f_{z} a_{p} - 0.07577 f_{z} v_{b} - 0.00805 f_{z} Q + 0.00295 f_{z} C \\ - 0.00548 a_{e} a_{p} + 0.00492 a_{e} v_{b} - 0.00173 a_{e} Q - 0.00555 a_{e} C \\ + 0.01014 a_{p} v_{b} + 0.00392 a_{p} Q - 0.00545 a_{p} C \end{array}

\begin{array}{l} R_{t} (x, z) = 3.0457 + 0.0385 v_{c} + 0.2939 f_{z} - 0.0215 a_{e} + 0.1234 a_{p} + 0.715 v_{b} \\ - 0.1067 Q - 0.0861 C + 0.29025 v_{c}^{2} + 0.3838 f_{z}^{2} + 0.3259 a_{e}^{2} + 0.2614 a_{p}^{2} \\ + 0.4954 v_{c} f_{z} - 0.0688 v_{c} a_{e} - 0.0275 v_{c} a_{p} + 0.2749 v_{c} v_{b} + 0.0009 v_{c} Q \\ - 0.0527 v_{c} C - 0.0219 f_{z} a_{e} + 0.0867 f_{z} a_{p} - 0.2908 f_{z} v_{b} + 0.1223 f_{z} Q \\ + 0.0069 f_{z} C + 0.0477 a_{e} a_{p} + 0.1158 a_{e} v_{b} - 0.0047 a_{e} Q - 0.0248 a_{e} C \\ + 0.1205 a_{p} v_{b} + 0.0054 a_{p} Q - 0.0647 a_{p} C \end{array}

\begin{array}{l} μ (R_{a}) (x, z) = 0.42560 + 0.01597 v_{c} + 0.05574 f_{z} + 0.00198 a_{e} + 0.00826 a_{p} + 0.04525 v_{c}^{2} + 0.06038 f_{z}^{2} + 0.06725 a_{e}^{2} \\ + 0.0563 a_{p}^{2} + 0.08814 v_{c} f_{z} - 0.00517 v_{c} a_{e} - 0.01127 v_{c} a_{p} + 0.00542 f_{z} a_{e} + 0.01033 f_{z} a_{p} - 0.00548 a_{e} a_{p} \end{array}

\begin{array}{l} σ^{2} (R_{a}) = 0.02477 + 0.00969 v_{c} - 0.02006 f_{z} + 0.00149 a_{e} + 0.00234 a_{p} + 0.00123 v_{c}^{2} + 0.00581 f_{z}^{2} + 0.00006 a_{e}^{2} \\ + 0.00015 a_{p}^{2} - 0.00530 v_{c} f_{z} + 0.00033 v_{c} a_{e} + 0.00070 v_{c} a_{p} - 0.00075 f_{z} a_{e} - 0.00163 f_{z} a_{p} + 0.00015 a_{e} a_{p} \end{array}

\begin{array}{l} μ (R_{t}) = 3.0457 + 0.0385 v_{c} + 0.2939 f_{z} - 0.0215 a_{e} + 0.1234 a_{p} + 0.29025 v_{c}^{2} + 0.3838 f_{z}^{2} + 0.3259 a_{e}^{2} \\ + 0.2614 a_{p}^{2} + 0.4954 v_{c} f_{z} - 0.0688 v_{c} a_{e} - 0.0275 v_{c} a_{p} - 0.0219 f_{z} a_{e} + 0.0867 f_{z} a_{p} + 0.0477 a_{e} a_{p} \end{array}

\begin{array}{l} σ^{2} (R_{t}) = 0.66622 + 0.40199 v_{c} - 0.44313 f_{z} + 0.17087 a_{e} + 0.18230 a_{p} + 0.07835 v_{c}^{2} + 0.09957 f_{z}^{2} + 0.01405 a_{e}^{2} \\ + 0.01874 a_{p}^{2} - 0.16039 v_{c} f_{z} + 0.06627 v_{c} a_{e} + 0.07308 v_{c} a_{p} - 0.06884 f_{z} a_{e} - 0.06965 f_{z} a_{p} + 0.03107 a_{e} a_{p} \end{array}

[1] 3 wander.p.ribeiro@gmail.com

Brasil

Brasil

Optimization of duplex stainless steel UNS S32205 end milling with noise factor analysisy

Abstract