Mechanical Engineering Department
ME 406- Manufacturing and Design
Project A (Engineering Statistics and Manufacturing)
Title of the Project
Quality Control, Regression Analysis, and Models Fitting
Term 171
Class Section- xx
Project Team – Group X_X
xxxxxxxxx Name 1 (Group Coordinator)
xxxxxxxxx Name 2
xxxxxxxxx Name 3
xxxxxxxxx Name 4
Assigned on 13th November 2017
Due on 4th January 2018 (Before Exam starts)
Note Please Attempt each question as asked using the software where ever mentioned. Full Report generated by STATGRAPHICS Must be included in Problems 1 .All Excel sheets be included in PROBLEMS where Excel has been used such as in Q
Each problem should be started on separate page after pasting the the problem statement at the top of the page. Your Solution will be typewritten.
A hard copy as (WORD +EXCELL SHEETS) be provided along with a Hard copy in PDF format. Plus Software generated reports
A soft copy as a CD (WORD +EXCELL SHEETS) be provided along with a soft copy copy in PDF format. Plus Software generated reports. CD Must have mentioned that it is STSTISTICS PROJECT and it shoulf have All Project students Name and ID mentioned on CD and a on a text file inside the cD.
Project copies both word and PDF will be uploaded on WebCT as will be explained later.
For alpha distribution
Find
a) Plot F(t) versus t/C for =0.05 , 0.1.0.15,0.2 ,0.25 and 0.3 (all curves should be in one Figure for range of t/C varying from (0+=0.05) to 4). Hint use Normal Distribution Function(select True) of Excel subroutine for Z=-
b) Find pdf for t varying from -∞ to +∞ ,(note at t=0 function is undefined). Note
where
Z=-
c) Plot f(t) versus t/C for =0.05 , 0.1.0.15,0.2 ,0.25 and 0.3 .all curves in one Figure for range of t/C varying from (0+=0.05) to 4 . Hint use Normal Distribution Function (select False) of Excel subroutine for Z=-
d) Median value of T, t0.5
e) Quantile, tp which is the solution of F(tp)=p .
f) Mode of T, (value of t where
PROBLEM # 2 (1.0 point) Use EXCEL and attach all spreadsheet analysis with solution)
Fifty measurements of the ultimate tensile strength of wire are given in the accompanying table.
a) Group the data and make an appropriate normalized histogram (with total area of histogram be 1 ) to approximate the PDF.
b) Calculate and for the distribution from the ungrouped data.
c) Using and from part b, draw a normal distribution through the normalized histogram .histogram.
|
Ultimate Tensile Strength |
|
|
|
|
103,779 |
102,325 |
102,325 |
103,799 |
|
102,906 |
104,651 |
105,377 |
100,145 |
|
104,796 |
105,087 |
104,796 |
103,799 |
|
103,197 |
106,395 |
106,831 |
103,488 |
|
100,872 |
100,872 |
105,087 |
102,906 |
|
97,383 |
104,360 |
103,633 |
101,017 |
|
101,162 |
101,453 |
107,848 |
104,651 |
|
98,110 |
103,779 |
99,563 |
103,197 |
|
104,651 |
101,162 |
105,813 |
105,337 |
|
102,906 |
102,470 |
108,430 |
101,744 |
|
103,633 |
105,232 |
106,540 |
106,104 |
|
102,616 |
106,831 |
101,744 |
100,726 |
|
103,924 |
|
101,598 |
|
Source: Data from E. B. Haugen, Probabilistic Mechanical Design Wiley, New York, 1980
(c) Determine the mean, median, and mode from the ungrouped data.
(d) Determine the range and standard deviation from the ungrouped data
(e) Plot the cumulative frequency distribution on normal-probability paper, and determine the mean and standard deviation.
(f), for the data given in Table .what are the 95 percent confidence limits on the mean of the population?
PROBLEM # 3 (1.0 point) (Use EXCEL and attach all spreadsheet analysis with solution)
Three sets of identical twenty five fatigue specimens were tested at the three different level of stresses.. The number of cycles to failure. The results are expressed as log, were as follows.
|
TABLE 1: FATIGUE LIFE DATA |
|||
|
NUMBER OF CYCLES TO FAILURES |
|||
|
No. |
S1 |
S2 |
S3 |
|
380 MPa |
340 MPa |
300 MPa |
|
|
1 |
34200 |
125500 |
954000 |
|
2 |
37700 |
156900 |
959400 |
|
3 |
42000 |
173600 |
1194600 |
|
4 |
42300 |
176900 |
1240500 |
|
5 |
48200 |
179400 |
1250400 |
|
6 |
52500 |
188500 |
1285500 |
|
7 |
55900 |
195100 |
1410500 |
|
8 |
58300 |
208100 |
1495100 |
|
9 |
61700 |
211900 |
1518700 |
|
10 |
64700 |
224100 |
1544700 |
|
11 |
65000 |
226000 |
1551400 |
|
12 |
65500 |
253000 |
1585900 |
|
13 |
70400 |
255500 |
1639100 |
|
14 |
71000 |
259000 |
1683700 |
|
15 |
72400 |
274000 |
1926100 |
|
16 |
75200 |
292000 |
2011300 |
|
17 |
77400 |
300400 |
2171800 |
|
18 |
77800 |
302300 |
2391500 |
|
19 |
87800 |
308300 |
2569400 |
|
20 |
93400 |
406300 |
2674900 |
|
21 |
94000 |
420700 |
2921700 |
|
22 |
97200 |
428500 |
3046500 |
|
23 |
99600 |
664800 |
3105500 |
|
24 |
116700 |
776100 |
3523200 |
|
25 |
122500 |
793900 |
4311700 |
Assume that the data at each stress level (S1, S2 and S3) is lognormally distributed.
Using directly the data in table determine
· What is the mean fatigue life ( μ) and its standard deviation (σ )?
· What is the mean Ln of fatigue life ( μlnN) and its standard deviation Ln of fatigue life (σlnN)?
· What are the Parameters of Lognormal distributions at S1,S2and S3.
· Fit lognormal distribution to the data using linear regression model using Excel or Use Statgraphics to fit the lognormal models to data for each stress level and comment on how good the fit is.
PROBLEM # 4 (1.5 point)
Q4. (a) The lifetime of a mechanical switch produced by a company has been determined to have a population mean of μ = 2000 h and σ = 200 h. The temper of a phosphor bronze leaf spring in the switch is changed slightly by the supplier. To determine whether this has changed the product, a sample of 100 switches is tested to give the sample values and . Has there been a change in the product? (0.75 point)
Q4. (b) A vendor of steel wire advertises a mean breaking load of 10,000 lb. A sample of eight tests shows a mean breaking load of 9250 lb and a standard deviation of 110 lb. Do our tests support the vendor’s claim? (0.75 point)
PROBLEM # 5 Control Charts (1 point)
Problem 5-Refer your Text Book above ( See Ebook provided as text book)- -Solve with appropriate calculations, tables and charts
5.1-Problem 8.1 Parts (a) and (b) –P454
5.2 -Problem 8.28 Parts (a) and (b) –P470
PROBLEM # 6
Regression Analysis (MUST USE STATGRAPHICS_ ATTACH COMPLETE REPORT PLUS ONE PAGE SUMMARY OF EACH FITTED MODEL) 2 points
Developing Cutting Forces Empirical Models of a Counter Boring Process in Aluminum.
Counter boring is an operation to enlarge the hole made using drilling. Counter boring or finish boring is a deep hole drilling process that requires a work piece with a pre-existing bore. Counter boring is used to enlarge the drilled hole to the proper depth and machine a square shoulder on the bottom to secure maximum clamping action from the faster. The drilling used to produce a circular hole by removing solid metal. The counter bore tool has a guide, called a pilot, which keep it positioned correctly in the hole. Counter boring tools are often used on low power machines were a small diameter solid boring tool is used for the pre-bore and then a counter boring tool is used to finish the job. Counter boring is also used when there is a heat treat process required after the initial hole is drilled or if a stepped hole is required.
Pilot of diameter d , which is the predrilled hole size in the workpiece diameter of already drilled hole..
D Dia of the enlarged hole
Visit the link and download STATGRAPHICS FREE FOR 30 DAYS AND USE MULTIPLE REGRESSION MODULE (SEE EXAMPLES ON WEBSITE) TO DEVELOP FOLLOWING MODELS>
http://www.statgraphics.com/centurion-xvii
Regression Analysis http://www.statgraphics.com/regression-analysis
And Quality Control Module (PROICESS CAPABILITY BANALYSIS) from the link http://www.statgraphics.com/process-capability-analysis
Following are the results of Cutting Forces measurements experiments performed at KFUPM Workshop by Professor Anwar K Sheikh. The results are being shared for regression analysis learning objectives.
Cutting Force Fz as a Function of V,D,d and f
|
Fz Newton |
Speed , V mm/minutes |
Feed , f Mm/revolution |
d mm |
D mm |
Ln (FZ) |
Ln(Speed) |
Ln(feed) |
Ln(D) |
|
52 |
2463.007 |
0.03 |
3.5 |
6.5 |
3.951244 |
7.809138 |
-3.50656 |
1.252763 |
|
78 |
2463.007 |
0.05 |
3.5 |
6.5 |
4.356709 |
7.809138 |
-2.99573 |
1.252763 |
|
104 |
2463.007 |
0.08 |
3.5 |
6.5 |
4.644391 |
7.809138 |
-2.52573 |
1.252763 |
|
130 |
2463.007 |
0.12 |
3.5 |
6.5 |
4.867534 |
7.809138 |
-2.12026 |
1.252763 |
|
65 |
3903.426 |
0.03 |
3.5 |
6.5 |
4.174387 |
8.26961 |
-3.50656 |
1.252763 |
|
78 |
3903.426 |
0.05 |
3.5 |
6.5 |
4.356709 |
8.26961 |
-2.99573 |
1.252763 |
|
104 |
3903.426 |
0.08 |
3.5 |
6.5 |
4.644391 |
8.26961 |
-2.52573 |
1.252763 |
|
130 |
3903.426 |
0.12 |
3.5 |
6.5 |
4.867534 |
8.26961 |
-2.12026 |
1.252763 |
|
65 |
4948.004 |
0.03 |
3.5 |
6.5 |
4.174387 |
8.50674 |
-3.50656 |
1.252763 |
|
78 |
4948.004 |
0.05 |
3.5 |
6.5 |
4.356709 |
8.50674 |
-2.99573 |
1.252763 |
|
117 |
4948.004 |
0.08 |
3.5 |
6.5 |
4.762174 |
8.50674 |
-2.52573 |
1.252763 |
|
130 |
4948.004 |
0.12 |
3.5 |
6.5 |
4.867534 |
8.50674 |
-2.12026 |
1.252763 |
|
65 |
6157.516 |
0.03 |
3.5 |
6.5 |
4.174387 |
8.725429 |
-3.50656 |
1.252763 |
|
78 |
6157.516 |
0.05 |
3.5 |
6.5 |
4.356709 |
8.725429 |
-2.99573 |
1.252763 |
|
104 |
6157.516 |
0.08 |
3.5 |
6.5 |
4.644391 |
8.725429 |
-2.52573 |
1.252763 |
|
130 |
6157.516 |
0.12 |
3.5 |
6.5 |
4.867534 |
8.725429 |
-2.12026 |
1.252763 |
|
72 |
7806.851 |
0.03 |
3.5 |
6.5 |
4.276666 |
8.962757 |
-3.50656 |
1.252763 |
|
85 |
7806.851 |
0.05 |
3.5 |
6.5 |
4.442651 |
8.962757 |
-2.99573 |
1.252763 |
|
111 |
7806.851 |
0.08 |
3.5 |
6.5 |
4.70953 |
8.962757 |
-2.52573 |
1.252763 |
|
130 |
7806.851 |
0.12 |
3.5 |
6.5 |
4.867534 |
8.962757 |
-2.12026 |
1.252763 |
|
78 |
2463.007 |
0.03 |
5.5 |
10 |
4.356709 |
7.809138 |
-3.50656 |
1.704748 |
|
104 |
2463.007 |
0.05 |
5.5 |
10 |
4.644391 |
7.809138 |
-2.99573 |
1.704748 |
|
130 |
2463.007 |
0.08 |
5.5 |
10 |
4.867534 |
7.809138 |
-2.52573 |
1.704748 |
|
182 |
2463.007 |
0.12 |
5.5 |
10 |
5.204007 |
7.809138 |
-2.12026 |
1.704748 |
|
84 |
3903.426 |
0.03 |
5.5 |
10 |
4.430817 |
8.26961 |
-3.50656 |
1.704748 |
|
110 |
3903.426 |
0.05 |
5.5 |
10 |
4.70048 |
8.26961 |
-2.99573 |
1.704748 |
|
143 |
3903.426 |
0.08 |
5.5 |
10 |
4.962845 |
8.26961 |
-2.52573 |
1.704748 |
|
182 |
3903.426 |
0.12 |
5.5 |
10 |
5.204007 |
8.26961 |
-2.12026 |
1.704748 |
|
91 |
4948.004 |
0.03 |
5.5 |
10 |
4.51086 |
8.50674 |
-3.50656 |
1.704748 |
|
117 |
4948.004 |
0.05 |
5.5 |
10 |
4.762174 |
8.50674 |
-2.99573 |
1.704748 |
|
130 |
4948.004 |
0.08 |
5.5 |
10 |
4.867534 |
8.50674 |
-2.52573 |
1.704748 |
|
182 |
4948.004 |
0.12 |
5.5 |
10 |
5.204007 |
8.50674 |
-2.12026 |
1.704748 |
|
78 |
6157.516 |
0.03 |
5.5 |
10 |
4.356709 |
8.725429 |
-3.50656 |
1.704748 |
|
104 |
6157.516 |
0.05 |
5.5 |
10 |
4.644391 |
8.725429 |
-2.99573 |
1.704748 |
|
143 |
6157.516 |
0.08 |
5.5 |
10 |
4.962845 |
8.725429 |
-2.52573 |
1.704748 |
|
195 |
6157.516 |
0.12 |
5.5 |
10 |
5.273 |
8.725429 |
-2.12026 |
1.704748 |
|
91 |
7806.851 |
0.03 |
5.5 |
10 |
4.51086 |
8.962757 |
-3.50656 |
1.704748 |
|
117 |
7806.851 |
0.05 |
5.5 |
10 |
4.762174 |
8.962757 |
-2.99573 |
1.704748 |
|
143 |
7806.851 |
0.08 |
5.5 |
10 |
4.962845 |
8.962757 |
-2.52573 |
1.704748 |
|
195 |
7806.851 |
0.12 |
5.5 |
10 |
5.273 |
8.962757 |
-2.12026 |
1.704748 |
|
117 |
2463.007 |
0.03 |
7.5 |
15 |
4.762174 |
7.809138 |
-3.50656 |
2.014903 |
|
143 |
2463.007 |
0.05 |
7.5 |
15 |
4.962845 |
7.809138 |
-2.99573 |
2.014903 |
|
195 |
2463.007 |
0.08 |
7.5 |
15 |
5.273 |
7.809138 |
-2.52573 |
2.014903 |
|
234 |
2463.007 |
0.12 |
7.5 |
15 |
5.455321 |
7.809138 |
-2.12026 |
2.014903 |
|
123 |
3903.426 |
0.03 |
7.5 |
15 |
4.812184 |
8.26961 |
-3.50656 |
2.014903 |
|
156 |
3903.426 |
0.05 |
7.5 |
15 |
5.049856 |
8.26961 |
-2.99573 |
2.014903 |
|
208 |
3903.426 |
0.08 |
7.5 |
15 |
5.337538 |
8.26961 |
-2.52573 |
2.014903 |
|
234 |
3903.426 |
0.12 |
7.5 |
15 |
5.455321 |
8.26961 |
-2.12026 |
2.014903 |
|
123 |
4948.004 |
0.03 |
7.5 |
15 |
4.812184 |
8.50674 |
-3.50656 |
2.014903 |
|
169 |
4948.004 |
0.05 |
7.5 |
15 |
5.129899 |
8.50674 |
-2.99573 |
2.014903 |
|
208 |
4948.004 |
0.08 |
7.5 |
15 |
5.337538 |
8.50674 |
-2.52573 |
2.014903 |
|
247 |
4948.004 |
0.12 |
7.5 |
15 |
5.509388 |
8.50674 |
-2.12026 |
2.014903 |
|
130 |
6157.516 |
0.03 |
7.5 |
15 |
4.867534 |
8.725429 |
-3.50656 |
2.014903 |
|
169 |
6157.516 |
0.05 |
7.5 |
15 |
5.129899 |
8.725429 |
-2.99573 |
2.014903 |
|
208 |
6157.516 |
0.08 |
7.5 |
15 |
5.337538 |
8.725429 |
-2.52573 |
2.014903 |
|
247 |
6157.516 |
0.12 |
7.5 |
15 |
5.509388 |
8.725429 |
-2.12026 |
2.014903 |
|
143 |
7806.851 |
0.03 |
7.5 |
15 |
4.962845 |
8.962757 |
-3.50656 |
2.014903 |
|
182 |
7806.851 |
0.05 |
7.5 |
15 |
5.204007 |
8.962757 |
-2.99573 |
2.014903 |
|
208 |
7806.851 |
0.08 |
7.5 |
15 |
5.337538 |
8.962757 |
-2.52573 |
2.014903 |
|
247 |
7806.851 |
0.12 |
7.5 |
15 |
5.509388 |
8.962757 |
-2.12026 |
2.014903 |
|
156 |
2463.007 |
0.03 |
9.5 |
18 |
5.049856 |
7.809138 |
-3.50656 |
2.251292 |
|
208 |
2463.007 |
0.05 |
9.5 |
18 |
5.337538 |
7.809138 |
-2.99573 |
2.251292 |
|
260 |
2463.007 |
0.08 |
9.5 |
18 |
5.560682 |
7.809138 |
-2.52573 |
2.251292 |
|
338 |
2463.007 |
0.12 |
9.5 |
18 |
5.823046 |
7.809138 |
-2.12026 |
2.251292 |
|
208 |
3903.426 |
0.03 |
9.5 |
18 |
5.337538 |
8.26961 |
-3.50656 |
2.251292 |
|
234 |
3903.426 |
0.05 |
9.5 |
18 |
5.455321 |
8.26961 |
-2.99573 |
2.251292 |
|
260 |
3903.426 |
0.08 |
9.5 |
18 |
5.560682 |
8.26961 |
-2.52573 |
2.251292 |
|
364 |
3903.426 |
0.12 |
9.5 |
18 |
5.897154 |
8.26961 |
-2.12026 |
2.251292 |
|
208 |
4948.004 |
0.03 |
9.5 |
18 |
5.337538 |
8.50674 |
-3.50656 |
2.251292 |
|
234 |
4948.004 |
0.05 |
9.5 |
18 |
5.455321 |
8.50674 |
-2.99573 |
2.251292 |
|
260 |
4948.004 |
0.08 |
9.5 |
18 |
5.560682 |
8.50674 |
-2.52573 |
2.251292 |
|
364 |
4948.004 |
0.12 |
9.5 |
18 |
5.897154 |
8.50674 |
-2.12026 |
2.251292 |
|
208 |
6157.516 |
0.03 |
9.5 |
18 |
5.337538 |
8.725429 |
-3.50656 |
2.251292 |
|
260 |
6157.516 |
0.05 |
9.5 |
18 |
5.560682 |
8.725429 |
-2.99573 |
2.251292 |
|
286 |
6157.516 |
0.08 |
9.5 |
18 |
5.655992 |
8.725429 |
-2.52573 |
2.251292 |
|
338 |
6157.516 |
0.12 |
9.5 |
18 |
5.823046 |
8.725429 |
-2.12026 |
2.251292 |
|
234 |
7806.851 |
0.03 |
9.5 |
18 |
5.455321 |
8.962757 |
-3.50656 |
2.251292 |
|
286 |
7806.851 |
0.05 |
9.5 |
18 |
5.655992 |
8.962757 |
-2.99573 |
2.251292 |
|
312 |
7806.851 |
0.08 |
9.5 |
18 |
5.743003 |
8.962757 |
-2.52573 |
2.251292 |
Moment Mz as a Function of V,D,d and f
|
Mz Newton-meter |
Speed , V mm/minutes |
Feed , f Mm/ revolution |
d mm |
D mm |
Ln (Mz) |
Ln(Speed) |
Ln(feed) |
Ln(D) |
|
|
39 |
2463.007 |
0.03 |
3.5 |
6.5 |
3.663562 |
7.809138 |
-3.50656 |
1.252763 |
|
|
59 |
2463.007 |
0.05 |
3.5 |
6.5 |
4.077537 |
7.809138 |
-2.99573 |
1.252763 |
|
|
72 |
2463.007 |
0.08 |
3.5 |
6.5 |
4.276666 |
7.809138 |
-2.52573 |
1.252763 |
|
|
104 |
2463.007 |
0.12 |
3.5 |
6.5 |
4.644391 |
7.809138 |
-2.12026 |
1.252763 |
|
|
39 |
3903.426 |
0.03 |
3.5 |
6.5 |
3.663562 |
8.26961 |
-3.50656 |
1.252763 |
|
|
52 |
3903.426 |
0.05 |
3.5 |
6.5 |
3.951244 |
8.26961 |
-2.99573 |
1.252763 |
|
|
78 |
3903.426 |
0.08 |
3.5 |
6.5 |
4.356709 |
8.26961 |
-2.52573 |
1.252763 |
|
|
117 |
3903.426 |
0.12 |
3.5 |
6.5 |
4.762174 |
8.26961 |
-2.12026 |
1.252763 |
|
|
39 |
4948.004 |
0.03 |
3.5 |
6.5 |
3.663562 |
8.50674 |
-3.50656 |
1.252763 |
|
|
59 |
4948.004 |
0.05 |
3.5 |
6.5 |
4.077537 |
8.50674 |
-2.99573 |
1.252763 |
|
|
78 |
4948.004 |
0.08 |
3.5 |
6.5 |
4.356709 |
8.50674 |
-2.52573 |
1.252763 |
|
|
117 |
4948.004 |
0.12 |
3.5 |
6.5 |
4.762174 |
8.50674 |
-2.12026 |
1.252763 |
|
|
39 |
6157.516 |
0.03 |
3.5 |
6.5 |
3.663562 |
8.725429 |
-3.50656 |
1.252763 |
|
|
52 |
6157.516 |
0.05 |
3.5 |
6.5 |
3.951244 |
8.725429 |
-2.99573 |
1.252763 |
|
|
78 |
6157.516 |
0.08 |
3.5 |
6.5 |
4.356709 |
8.725429 |
-2.52573 |
1.252763 |
|
|
124 |
6157.516 |
0.12 |
3.5 |
6.5 |
4.820282 |
8.725429 |
-2.12026 |
1.252763 |
|
|
39 |
7806.851 |
0.03 |
3.5 |
6.5 |
3.663562 |
8.962757 |
-3.50656 |
1.252763 |
|
|
59 |
7806.851 |
0.05 |
3.5 |
6.5 |
4.077537 |
8.962757 |
-2.99573 |
1.252763 |
|
|
72 |
7806.851 |
0.08 |
3.5 |
6.5 |
4.276666 |
8.962757 |
-2.52573 |
1.252763 |
|
|
117 |
7806.851 |
0.12 |
3.5 |
6.5 |
4.762174 |
8.962757 |
-2.12026 |
1.252763 |
|
|
52 |
2463.007 |
0.03 |
5.5 |
10 |
3.951244 |
7.809138 |
-3.50656 |
1.704748 |
|
|
72 |
2463.007 |
0.05 |
5.5 |
10 |
4.276666 |
7.809138 |
-2.99573 |
1.704748 |
|
|
98 |
2463.007 |
0.08 |
5.5 |
10 |
4.584967 |
7.809138 |
-2.52573 |
1.704748 |
|
|
163 |
2463.007 |
0.12 |
5.5 |
10 |
5.09375 |
7.809138 |
-2.12026 |
1.704748 |
|
|
65 |
3903.426 |
0.03 |
5.5 |
10 |
4.174387 |
8.26961 |
-3.50656 |
1.704748 |
|
|
84 |
3903.426 |
0.05 |
5.5 |
10 |
4.430817 |
8.26961 |
-2.99573 |
1.704748 |
|
|
110 |
3903.426 |
0.08 |
5.5 |
10 |
4.70048 |
8.26961 |
-2.52573 |
1.704748 |
|
|
169 |
3903.426 |
0.12 |
5.5 |
10 |
5.129899 |
8.26961 |
-2.12026 |
1.704748 |
|
|
65 |
4948.004 |
0.03 |
5.5 |
10 |
4.174387 |
8.50674 |
-3.50656 |
1.704748 |
|
|
98 |
4948.004 |
0.05 |
5.5 |
10 |
4.584967 |
8.50674 |
-2.99573 |
1.704748 |
|
|
110 |
4948.004 |
0.08 |
5.5 |
10 |
4.70048 |
8.50674 |
-2.52573 |
1.704748 |
|
|
169 |
4948.004 |
0.12 |
5.5 |
10 |
5.129899 |
8.50674 |
-2.12026 |
1.704748 |
|
|
65 |
6157.516 |
0.03 |
5.5 |
10 |
4.174387 |
8.725429 |
-3.50656 |
1.704748 |
|
|
98 |
6157.516 |
0.05 |
5.5 |
10 |
4.584967 |
8.725429 |
-2.99573 |
1.704748 |
|
|
117 |
6157.516 |
0.08 |
5.5 |
10 |
4.762174 |
8.725429 |
-2.52573 |
1.704748 |
|
|
169 |
6157.516 |
0.12 |
5.5 |
10 |
5.129899 |
8.725429 |
-2.12026 |
1.704748 |
|
|
65 |
7806.851 |
0.03 |
5.5 |
10 |
4.174387 |
8.962757 |
-3.50656 |
1.704748 |
|
|
98 |
7806.851 |
0.05 |
5.5 |
10 |
4.584967 |
8.962757 |
-2.99573 |
1.704748 |
|
|
130 |
7806.851 |
0.08 |
5.5 |
10 |
4.867534 |
8.962757 |
-2.52573 |
1.704748 |
|
|
163 |
7806.851 |
0.12 |
5.5 |
10 |
5.09375 |
8.962757 |
-2.12026 |
1.704748 |
|
|
81 |
2463.007 |
0.03 |
7.5 |
15 |
4.394449 |
7.809138 |
-3.50656 |
2.014903 |
|
|
130 |
2463.007 |
0.05 |
7.5 |
15 |
4.867534 |
7.809138 |
-2.99573 |
2.014903 |
|
|
195 |
2463.007 |
0.08 |
7.5 |
15 |
5.273 |
7.809138 |
-2.52573 |
2.014903 |
|
|
260 |
2463.007 |
0.12 |
7.5 |
15 |
5.560682 |
7.809138 |
-2.12026 |
2.014903 |
|
|
104 |
3903.426 |
0.03 |
7.5 |
15 |
4.644391 |
8.26961 |
-3.50656 |
2.014903 |
|
|
143 |
3903.426 |
0.05 |
7.5 |
15 |
4.962845 |
8.26961 |
-2.99573 |
2.014903 |
|
|
195 |
3903.426 |
0.08 |
7.5 |
15 |
5.273 |
8.26961 |
-2.52573 |
2.014903 |
|
|
260 |
3903.426 |
0.12 |
7.5 |
15 |
5.560682 |
8.26961 |
-2.12026 |
2.014903 |
|
|
117 |
4948.004 |
0.03 |
7.5 |
15 |
4.762174 |
8.50674 |
-3.50656 |
2.014903 |
|
|
156 |
4948.004 |
0.05 |
7.5 |
15 |
5.049856 |
8.50674 |
-2.99573 |
2.014903 |
|
|
221 |
4948.004 |
0.08 |
7.5 |
15 |
5.398163 |
8.50674 |
-2.52573 |
2.014903 |
|
|
260 |
4948.004 |
0.12 |
7.5 |
15 |
5.560682 |
8.50674 |
-2.12026 |
2.014903 |
|
|
130 |
6157.516 |
0.03 |
7.5 |
15 |
4.867534 |
8.725429 |
-3.50656 |
2.014903 |
|
|
156 |
6157.516 |
0.05 |
7.5 |
15 |
5.049856 |
8.725429 |
-2.99573 |
2.014903 |
|
|
195 |
6157.516 |
0.08 |
7.5 |
15 |
5.273 |
8.725429 |
-2.52573 |
2.014903 |
|
|
286 |
6157.516 |
0.12 |
7.5 |
15 |
5.655992 |
8.725429 |
-2.12026 |
2.014903 |
|
|
130 |
7806.851 |
0.03 |
7.5 |
15 |
4.867534 |
8.962757 |
-3.50656 |
2.014903 |
|
|
169 |
7806.851 |
0.05 |
7.5 |
15 |
5.129899 |
8.962757 |
-2.99573 |
2.014903 |
|
|
221 |
7806.851 |
0.08 |
7.5 |
15 |
5.398163 |
8.962757 |
-2.52573 |
2.014903 |
|
|
299 |
7806.851 |
0.12 |
7.5 |
15 |
5.700444 |
8.962757 |
-2.12026 |
2.014903 |
|
|
221 |
2463.007 |
0.03 |
9.5 |
18 |
5.398163 |
7.809138 |
-3.50656 |
2.251292 |
|
|
260 |
2463.007 |
0.05 |
9.5 |
18 |
5.560682 |
7.809138 |
-2.99573 |
2.251292 |
|
|
357 |
2463.007 |
0.08 |
9.5 |
18 |
5.877736 |
7.809138 |
-2.52573 |
2.251292 |
|
|
487 |
2463.007 |
0.12 |
9.5 |
18 |
6.188264 |
7.809138 |
-2.12026 |
2.251292 |
|
|
227 |
3903.426 |
0.03 |
9.5 |
18 |
5.42495 |
8.26961 |
-3.50656 |
2.251292 |
|
|
325 |
3903.426 |
0.05 |
9.5 |
18 |
5.783825 |
8.26961 |
-2.99573 |
2.251292 |
|
|
357 |
3903.426 |
0.08 |
9.5 |
18 |
5.877736 |
8.26961 |
-2.52573 |
2.251292 |
|
|
487 |
3903.426 |
0.12 |
9.5 |
18 |
6.188264 |
8.26961 |
-2.12026 |
2.251292 |
|
|
195 |
4948.004 |
0.03 |
9.5 |
18 |
5.273 |
8.50674 |
-3.50656 |
2.251292 |
|
|
292 |
4948.004 |
0.05 |
9.5 |
18 |
5.676754 |
8.50674 |
-2.99573 |
2.251292 |
|
|
357 |
4948.004 |
0.08 |
9.5 |
18 |
5.877736 |
8.50674 |
-2.52573 |
2.251292 |
|
|
520 |
4948.004 |
0.12 |
9.5 |
18 |
6.253829 |
8.50674 |
-2.12026 |
2.251292 |
|
|
292 |
6157.516 |
0.03 |
9.5 |
18 |
5.676754 |
8.725429 |
-3.50656 |
2.251292 |
|
|
445 |
6157.516 |
0.05 |
9.5 |
18 |
6.098074 |
8.725429 |
-2.99573 |
2.251292 |
|
|
650 |
6157.516 |
0.08 |
9.5 |
18 |
6.476972 |
8.725429 |
-2.52573 |
2.251292 |
|
|
747 |
6157.516 |
0.12 |
9.5 |
18 |
6.616065 |
8.725429 |
-2.12026 |
2.251292 |
|
|
357 |
7806.851 |
0.03 |
9.5 |
18 |
5.877736 |
8.962757 |
-3.50656 |
2.251292 |
|
|
487 |
7806.851 |
0.05 |
9.5 |
18 |
6.188264 |
8.962757 |
-2.99573 |
2.251292 |
|
|
650 |
7806.851 |
0.08 |
9.5 |
18 |
6.476972 |
8.962757 |
-2.52573 |
2.251292 |
Using STATGRAPHICS -MULTIPLE LINEAR REGRESSION MODULE develop the empirical model for cutting force Fz and Torque (Moment) Mz can be writing as following
Find A,f ,b and c d e etc in Fz model using first data table ,and Find B,d,e,f d using second Data table for each of the odel.. Write one page summary based upon completer regression report generated by STATGRAPHICS for each fitted model .Its goodness of fit as measured by R2 values and other important coefficients tabulated and plotted in the report. (Attach PDF copy of each full report of STATGRAPHICS output and your EXCEL File used as input data.
c
b
a
V
D
f
A
Fz
´
´
´
=
f
e
d
V
D
f
B
Mz
´
´
´
=
c
b
a
V
d
D
f
A
Fz
´
–
´
´
=
)
(
2
2
)
(
2
2
d
D
–
f
e
d
V
d
D
f
B
Mz
´
–
´
´
=
)
(
2
2
)
(
2
2
d
D
–