Question

Turbochargers Are Us, a new start-up company, hires you to design their new turbocharger. They explain that they want to replace their metallic superalloy turbocharger with a high-tech ceramic which is much lighter for the same configuration. You decide that silicon nitride would be a good choice and you ask Ceramic Turbochargers, Inc. to supply you with strength bars made from their grade 2020 SisN4. They send you 25 strength bars which you break in four-point bending, using a 40 mm outer support span and a 20 mm inner loading span, obtaining the following data: Bar Width (mm) 6.02 6.00 5.98 + Thickness (mm) 3.99 4.00 3.99 4.04 4.05 4.00 4.01 4.02 3.97 3.96 3.97 4.05 4.00 4.01 3.99 3.98 4.03 4.01 Load (N) 2510 2615 2375 2865 2575 2605 2810 2595 2490 2650 2705 2765 2680 2725 2830 2730 2565 2650 2650 5.99 6.00 6.01 6.01 5.95 5.99 5.98 6.05 6.00 6.02 5.98 6.03 5.95 6.04 5.96 5.97 6.02 6.01 6.00 6.00 6.04 6.02 12 13 14 16 18 19 4.05 20 2745 22 4.00 4.00 3.99 3.98 3.95 4.05 2895 2525 2660 2680 2640 24 25 Answer the following questions using Excel, showing all calculations on your Excel spreadsheet:

Answer 1

All data in excel format up to strength calculation

Part number	Width(mm)	Thichness(mm)	Load(N)	Moment(M)	MOI	Y	Strength
1	6.02	3.99	2510	25100	31.86647	1.995	1571.385
2	6	4	2615	26150	32	2	1634.375
3	5.98	3.99	2375	23750	31.65473	1.995	1496.814
4	5.99	4.04	2865	28650	32.91468	2.02	1758.273
5	6	4.05	2575	25750	33.21506	2.025	1569.883
6	6.01	4	2605	26050	32.05333	2	1625.416
7	6.01	4.01	2810	28100	32.29433	2.005	1744.594
8	5.95	4.02	2595	25950	32.21172	2.01	1619.271
9	5.99	3.97	2490	24900	31.23324	1.985	1582.497
10	5.98	3.96	2650	26500	30.94607	1.98	1695.53
11	6.05	3.97	2705	27050	31.5461	1.985	1702.088
12	6	4.05	2765	27650	33.21506	2.025	1685.719
13	6.02	4	2680	26800	32.10667	2	1669.435
14	5.98	4.01	2725	27250	32.13313	2.005	1700.309
15	6.03	3.99	2830	28300	31.9194	1.995	1768.783
16	5.95	3.98	2730	27300	31.25971	1.99	1737.924
17	6.04	4.03	2565	25650	32.94358	2.015	1568.887
18	5.96	4.01	2650	26500	32.02566	2.005	1659.06
19	5.97	4.05	2650	26500	33.04899	2.025	1623.726
20	6.02	4	2745	27450	32.10667	2	1709.925
21	6.01	4	2895	28950	32.05333	2	1806.364
22	6	3.99	2525	25250	31.7606	1.995	1586.045
23	6	3.98	2660	26600	31.5224	1.99	1679.251
24	6.04	3.95	2680	26800	31.02037	1.975	1706.298
25	6.02	4.05	2640	26400	33.32578	2.025	1604.164

Ascending order of strength with failure and graph claculation

Part number	Strength	Rank	F	ln(strength)	Y=ln(ln(1/1-F))
3	1496.814181	1	0.02	7.311094249	-3.901938658
17	1568.886727	2	0.06	7.358121556	-2.782632533
5	1569.88264	3	0.1	7.358756144	-2.250367327
1	1571.385311	4	0.14	7.359712873	-1.891649046
9	1582.496512	5	0.18	7.36675895	-1.617213369
22	1586.045314	6	0.22	7.368998973	-1.392467941
25	1604.163534	7	0.26	7.380357737	-1.20029593
8	1619.27101	8	0.3	7.389731333	-1.030930433
19	1623.726007	9	0.34	7.392478792	-0.878235496
6	1625.415973	10	0.38	7.393519046	-0.738069652
2	1634.375	11	0.42	7.399015747	-0.607470205
18	1659.060102	12	0.46	7.414006517	-0.484206187
13	1669.435216	13	0.5	7.420240654	-0.366512921
23	1679.250524	14	0.54	7.426102856	-0.252921561
12	1685.71864	15	0.58	7.429947245	-0.142139113
10	1695.530352	16	0.62	7.435750863	-0.032953009
14	1700.308899	17	0.66	7.438565219	0.075858268
11	1702.088477	18	0.7	7.439611292	0.185626759
24	1706.298129	19	0.74	7.442081466	0.297934571
20	1709.925249	20	0.78	7.444204935	0.414839519
16	1737.924027	21	0.82	7.460446592	0.539295539
7	1744.593914	22	0.86	7.464277093	0.676058424
4	1758.273069	23	0.9	7.472087395	0.834032445
15	1768.783109	24	0.94	7.47804708	1.034397526
21	1806.364393	25	0.98	7.499071481	1.364054633

In(strength) vs Y 2 y = 26.697x - 198.49.- 1 7.3 7.35 7.4 7.45 7.5 7.55

From regression line equation slope is 26.697

Characterstic strength is given by putting Y as 0 in regression line equation

ln(strength)=198.49/26.697=7.4349

strength=1694.118mpa

Strength at F=0.5 can be found from table=1669.43

mean strength= sum of all strength/25=41506.016/25=1660.24mpa