Optimization of joining HDPE rods by continuous drive friction welding

Figures & Tables

RS (rpm)	Regression equation
082	Short=1.06−0.0717tf+0.00064Ff+0.000057tf2−0.000001Ff2+0.000057tf×Ff {\rm{Short}} = 1.06 - 0.0717{t_f} + 0.00064{F_f} + 0.000057t_f^2 - 0.000001F_f^2 + 0.000057{t_f} \times {F_f}
165	Short=−0.60−0.0400tf+0.00147Ff+0.000057tf2−0.000001Ff2+0.000057tf×Ff {\rm{Short}} = - 0.60 - 0.0400{t_f} + 0.00147{F_f} + 0.000057t_f^2 - 0.000001F_f^2 + 0.000057{t_f} \times {F_f}
300	Short=−2.43+0.0312tf+0.00183Ff+0.000057tf2−0.000001Ff2+0.000057tf×Ff {\rm{Short}} = - 2.43 + 0.0312{t_f} + 0.00183{F_f} + 0.000057t_f^2 - 0.000001F_f^2 + 0.000057{t_f} \times {F_f}
400	Short=−1.75+0.0494tf+0.00141Ff+0.000057tf2−0.000001Ff2+0.000057tf×Ff {\rm{Short}} = - 1.75 + 0.0494{t_f} + 0.00141{F_f} + 0.000057t_f^2 - 0.000001F_f^2 + 0.000057{t_f} \times {F_f}
550	Short=−4.07+0.1086tf+0.00290Ff+0.000057tf2−0.000001Ff2+0.000057tf×Ff {\rm{Short}} = - 4.07 + 0.1086{t_f} + 0.00290{F_f} + 0.000057t_f^2 - 0.000001F_f^2 + 0.000057{t_f} \times {F_f}

RS (rpm)	Regression equation
082	TS=−10.61+0.345tf+0.00959Ff−0.00159tf2−0.000002Ff2−0.000051tf×Ff {\rm{TS}} = - 10.61 + 0.345{t_f} + 0.00959{F_f} - 0.00159t_f^2 - 0.000002F_f^2 - 0.000051{t_f} \times {F_f}
165	TS=3.10+0.256tf+0.00532Ff−0.00159tf2−0.000002Ff2−0.000051tf×Ff {\rm{TS}} = 3.10 + 0.256{t_f} + 0.00532{F_f} - 0.00159t_f^2 - 0.000002F_f^2 - 0.000051{t_f} \times {F_f}
300	TS=−2.41+0.224tf+0.01012Ff−0.00159tf2−0.000002Ff2−0.000051tf×Ff {\rm{TS}} = - 2.41 + 0.224{t_f} + 0.01012{F_f} - 0.00159t_f^2 - 0.000002F_f^2 - 0.000051{t_f} \times {F_f}
400	TS=3.13+0.131tf+0.00842Ff−0.00159tf2−0.000002Ff2−0.000051tf×Ff {\rm{TS}} = 3.13 + 0.131{t_f} + 0.00842{F_f} - 0.00159t_f^2 - 0.000002F_f^2 - 0.000051{t_f} \times {F_f}
550	TS=−4.04+0.242tf+0.00859Ff−0.00159tf2−0.000002Ff2−0.000051tf×Ff {\rm{TS}} = - 4.04 + 0.242{t_f} + 0.00859{F_f} - 0.00159t_f^2 - 0.000002F_f^2 - 0.000051{t_f} \times {F_f}

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Model	17	492.737	28.9845	174.17	0.000
Linear	6	445.319	74.2199	446.00	0.000
t_f	1	97.663	97.6626	586.87	0.000
F_f	1	30.961	30.9606	186.05	0.000
RS	4	316.696	79.1740	475.77	0.000
Square	2	1.404	0.7021	4.22	0.021
tf2 t_f^2	1	0.006	0.0058	0.03	0.853
Ff2 F_f^2	1	1.352	1.3516	8.12	0.006
2-Way Interaction	9	46.014	5.1126	30.72	0.000
t_f*F_f	1	3.486	3.4861	20.95	0.000
t_f*RS	4	37.344	9.3360	56.10	0.000
F_f*RS	4	5.184	1.2959	7.79	0.000
Error	47	7.821	0.1664
Lack-of-Fit	27	5.567	0.2062	1.83	0.084
Pure Error	20	2.254	0.1127
Total	64	500.559

RS	Regression equation
082	Tmax=9.91+1.003tf+0.02847Ff−0.00481tf2−0.000006Ff2−0.000130tf×Ff {T_{max}} = 9.91 + 1.003{t_f} + 0.02847{F_f} - 0.00481t_f^2 - 0.000006F_f^2 - 0.000130{t_f} \times {F_f}
165	Tmax=16.14+0.998tf+0.03025Ff−0.00481tf2−0.000006Ff2−0.000130tf×Ff {T_{max}} = 16.14 + 0.998{t_f} + 0.03025{F_f} - 0.00481t_f^2 - 0.000006F_f^2 - 0.000130{t_f} \times {F_f}
300	Tmax=21.83+1.070tf+0.02963Ff−0.00481tf2−0.000006Ff2−0.000130tf×Ff {T_{max}} = 21.83 + 1.070{t_f} + 0.02963{F_f} - 0.00481t_f^2 - 0.000006F_f^2 - 0.000130{t_f} \times {F_f}
400	Tmax=22.80+1.111tf+0.02948Ff−0.00481tf2−0.000006Ff2−0.000130tf×Ff {T_{max}} = 22.80 + 1.111{t_f} + 0.02948{F_f} - 0.00481t_f^2 - 0.000006F_f^2 - 0.000130{t_f} \times {F_f}
550	Tmax=35.17+0.988tf+0.02932Ff−0.00481tf2−0.000006Ff2−0.000130tf×Ff {T_{max}} = 35.17 + 0.988{t_f} + 0.02932{F_f} - 0.00481t_f^2 - 0.000006F_f^2 - 0.000130{t_f} \times {F_f}

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Model	17	243.893	14.347	4.34	0.000
Linear	6	163.399	27.233	8.25	0.000
t_f	1	4.031	4.031	1.22	0.275
F_f	1	17.543	17.543	5.31	0.026
RS	4	141.825	35.456	10.74	0.000
Square	2	8.616	4.308	1.30	0.281
tf2 t_f^2	1	4.475	4.475	1.36	0.250
Ff2 F_f^2	1	5.260	5.260	1.59	0.213
2-Way Interaction	9	71.878	7.986	2.42	0.024
t_f *F_f	1	2.833	2.833	0.86	0.359
t_f *RS	4	42.229	10.557	3.20	0.021
F_f *RS	4	26.816	6.704	2.03	0.105
Error	47	155.205	3.302
Lack-of-Fit	27	108.605	4.022	1.73	0.106
Pure Error	20	46.600	2.330
Total	64	399.098

Run	Maximum temperature (°C)	Axial shortening (mm)	Tensile strength (MPa)	Run	Maximum temperature (°C)	Axial shortening (mm)	Tensile strength (MPa)
1	56.3	0.15	4.450	34	86.8	4.45	14.910
2	62.4	0.20	7.102	35	81.9	3.55	12.514
3	60.8	0.65	7.800	36	82.0	3.80	12.790
4	72.3	1.65	9.390	37	83.0	4.00	14.370
5	53.3	0.30	5.510	38	84.0	3.70	14.150
6	73.0	1.00	13.260	39	80.5	3.55	11.830
7	58.0	0.15	5.320	40	73.2	2.15	10.870
8	64.5	0.95	8.356	41	95.9	6.20	10.500
9	69.1	0.75	9.320	42	80.6	2.35	9.040
10	64.4	0.55	8.330	43	91.3	8.15	9.090
11	68.6	0.70	9.250	44	76.4	1.95	14.300
12	72.4	2.00	11.110	45	94.1	6.70	7.100
13	68.4	0.90	10.930	46	73.3	2.55	7.390
14	61.0	0.50	13.030	47	90.8	5.35	13.470
15	76.0	0.75	13.550	48	85.2	4.85	10.500
16	68.8	1.35	11.290	49	79.9	4.80	10.160
17	81.8	3.40	11.520	50	85.7	4.85	13.570
18	67.1	0.75	11.910	51	82.7	4.40	12.110
19	79.0	3.25	14.570	52	84.5	4.75	13.060
20	67.9	0.55	13.620	53	81.8	3.20	7.490
21	79.9	2.55	11.450	54	92.6	8.00	8.330
22	74.9	2.05	11.240	55	86.8	5.10	7.900
23	75.4	1.65	13.410	56	95.0	12.80	9.890
24	69.2	1.90	10.820	57	79.6	3.00	8.290
25	77.9	1.90	10.340	58	97.0	10.90	8.270
26	76.5	2.10	7.730	59	83.8	5.10	9.120
27	69.7	1.15	7.540	60	97.6	8.80	11.980
28	87.0	4.05	12.285	61	94.9	6.90	8.980
29	79.0	2.60	13.500	62	92.5	6.60	6.140
30	88.3	6.45	10.500	63	92.2	7.00	9.970
31	72.0	1.55	11.560	64	94.1	7.55	9.930
32	91.0	6.95	10.810	65	91.1	6.90	9.650
33	74.4	1.70	9.360

Property	Value
Melting temperature (°C)	126–135
Crystallization temperature (°C)	111.9
Density (g/cm³)	0.955
Thermal conductivity (W/mK)	0.35–0.49
Specific heat – solid (kJ/kg°C)	1.9
Tensile strength (MPa) at 23°C	23.0–29.5

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Model	17	7297.99	429.29	50.12	0.000
Linear	6	7162.50	1193.75	139.37	0.000
t_f	1	1510.42	1510.42	176.34	0.000
F_f	1	467.61	467.61	54.59	0.000
RS	4	5184.47	1296.12	151.32	0.000
Square	2	92.92	46.46	5.42	0.008
tf2 t_f^2	1	40.66	40.66	4.75	0.034
Ff2 F_f^2	1	63.98	63.98	7.47	0.009
2-Way Interaction	9	42.58	4.73	0.55	0.828
t_f*F_f	1	18.43	18.43	2.15	0.149
t_f*RS	4	20.98	5.24	0.61	0.656
F_f*RS	4	3.17	0.79	0.09	0.984
Error	47	402.56	8.57
Lack-of-Fit	27	287.51	10.65	1.85	0.080
Pure Error	20	115.06	5.75
Total	64	7700.56