Experimental study and multi-objective optimisation of CNC turning parameters of AL6061 materials

Figures & data

Table 1. Formula of signal-to-noise Ratio.

Signal-to-noise ratio	Goal of the experiment	Signal-to-noise ratio formula
Nominal is best:	When targeting a precise value	$\frac{S}{N}=10\ast log\frac{\underset{\_}{\bar{y}}}{s_y^2}$	(1)
Larger is better	When maximizing the response	$\frac{S}{N}=-10\ast \log \left(\frac{1}{n}\sum _{\mathit{i}=1}^n\frac{1}{y_i^2}\right)$	(2)
Smaller is better	When minimizing the response	$\frac{S}{N}=-10\ast \log \left(\frac{1}{n}\sum _{\mathit{i}=1}^n{y}_i^2\right)$	(3)

*Y is a performance measure; n is the number of experimental runs in each response.

Table 2. Control factors and their levels.

Control factor	Level 1	Level 2	Level 3
A. Feed rate (mm/rev)	0.05	0.1	0.2
B. Cutting speed (m/min)	150	175	200
C. Depth of cut (mm)	1	2	3

Figure 1. Workpieces after conducting experiment.

Figure 2. LB3000 ex II Okuma CNC lathe machine.

Figure 3. Chemical properties of AL6061.

Figure 4. (a). Mitutoyo SJ-210 portable surface roughness tester, (b) Digital scale SF-400D.

Table 3. L9 Taguchi design and experiment results.

Trial	Feed rate (mm/rev)	Cutting speed (m/min)	Cut depth (mm)	Material Removal Rate (cm3/s)			Surface Roughness (µm)			Signal to Noise
				MRR1	MRR2	MRR3	SR1	SR2	SR3	S/N_MRR	S/N_SR
1	0.05	150	1	0.0697	0.0698	0.0695	0.525	0.517	0.537	−23.141	5.574
2	0.05	175	2	0.1361	0.137	0.1345	0.592	0.581	0.606	−17.338	4.538
3	0.05	200	3	0.2593	0.2593	0.2613	0.607	0.57	0.566	−11.702	4.712
4	0.1	150	2	0.1731	0.174	0.178	2.386	2.438	2.468	−15.140	−7.715
5	0.1	175	3	0.4709	0.4809	0.475	2.187	2.151	2.129	−6.456	−6.672
6	0.1	200	1	0.2069	0.209	0.2077	2.241	2.268	2.313	−13.644	−7.137
7	0.2	150	3	0.6296	0.635	0.642	3.418	3.39	3.418	−3.938	−10.652
8	0.2	175	1	0.3982	0.395	0.3967	3.413	3.434	3.401	−8.033	−10.670
9	0.2	200	2	0.4667	0.468	0.465	3.462	3.433	3.392	−6.622	−10.704

Table 4. S/N response table for MRR and SR.

	Level	Feed Rate	Cutting Speed	Cut Depth
MRR	1	−17.394	−14.073	−14.939
	2	−11.747	−10.609	−13.033
	3	−6.198	−10.656	−7.365
	Delta	11.196	3.464	7.574
	Rank	1	3	2
SR	1	4.941	−4.264	−4.078
	2	−7.175	−4.268	−4.627
	3	−10.675	−4.376	−4.204
	Delta	15.616	0.112	0.549
	Rank	1	3	2

Figure 5. Main effect plot for signal-to-noise ratio of MRR and SR.

Table 5. ANOVA table for MRR and SR.

Source	DF	Adj SS	Adj MS	F-Value	P-Value	% Contribution
MRR
Feed rate	2	0.181322	0.090661	29.48	0.033	63.7%
Cutting speed	2	0.002747	0.001373	0.45	0.691	1.0%
Cut depth	2	0.094313	0.047157	15.33	0.061	33.1%
Error	2	0.006151	0.003075			2.2%
Total	8	0.284532				100.0%
SR
Feed rate	2	12.3666	6.18332	739.55	0.001	99.7%
Cutting speed	2	0.0068	0.00341	0.41	0.711	0.1%
Cut depth	2	0.0173	0.00863	1.03	0.492	0.1%
Error	2	0.0167	0.00836			0.1%
Total	8	12.4074				100.0%

Figure 6. Main effect plot for means of MRR and SR (software minitab 19).

Figure 7. Contour and 3D surface plots depicting the main factor interactions on MRR (software minitab 19).

Figure 8. Pareto front (software MATLAB 2018a).

Table 6. Pareto-optimal set.

Feed rate (mm/rev)	Cutting speed (m/min)	Cut depth) (mm)	MRR (cm3/s)	SR (µm)
0.2000	181.3568	2.9932	0.7666	3.3441
0.0500	177.4374	1.0064	0.1580	0.5659
0.0814	179.3940	2.9909	0.4132	1.7307
0.0518	179.5929	2.9565	0.3162	0.6639
0.0628	181.2132	2.9732	0.3523	1.0860
0.1301	180.6370	2.9913	0.5576	2.9039
0.0504	177.6305	2.3840	0.1928	0.6039
0.1242	180.4687	2.9478	0.5266	2.8021
0.0892	180.0277	2.9212	0.4159	1.9643
0.0748	181.0405	2.9663	0.3861	1.5110
0.0507	178.5371	2.9047	0.2999	0.6209
0.1676	181.1212	2.9601	0.6588	3.3248
0.1428	180.7937	2.9102	0.5693	3.0959
0.0500	177.4374	1.0064	0.1580	0.5659
0.0673	180.6193	2.9796	0.3679	1.2534
0.0948	180.7970	2.9775	0.4485	2.1207
0.1701	180.7312	2.9878	0.6754	3.3371
0.1478	180.0831	2.9143	0.5850	3.1594

Data availability statement

The experimental datasets obtained from this research work and then the analysed results during the current study are available from the corresponding author on reasonable request.