• Like
17
Upcoming SlideShare
Loading in...5
×
Uploaded on

 

More in: Technology , Education
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
311
On Slideshare
0
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
1
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1. Treating simulation data with mathematical functions using chi-square technique **…formulas achieved by using Chi - square based Java applets on http://csbsju.edu *…relationship btw outputs ( filling,spread ) and inputs ( thickness red.,friction,…)
  • 2. Thickness reduction ( r ) variation Rolling model Filling factor = H 1 – t (H 1 = central height)
  • 3. Fixed condition with: friction 0.15; sample width 40mm, thickness 5mm, groove 10mm and 20 degrees. 0.00 40.00 5.00 0 1.22 42.36 4.22 40 1.07 41.52 4.32 35 0.95 41.27 4.45 30 0.76 41.06 4.51 25 0.59 41.03 4.59 20 0.24 40.33 4.74 10 Filling factor (as drawn) S (mm) spread H r (mm) (central) Thickness reduction,%
  • 4. Other fixed conditions, relationship btw Hr and r (thickness red.) Drawn with Origin 7.0 from simulation results The central (max) height
  • 5. Linear model : y = a + bx ( http://www.physics.csbsju.edu/stats/WAPP.html ) Hr = 4.992 – 0.019r Test with r = 40  Hr = 4.992 – 0.019 x 40 = 4.232 Measured H r (40%) = 4.22 mm  error (relative) = (4.232 – 4.22)/4.22 = 0.28% Test with r = 10  Hr = 4.992 – 0.019 x 10 = 4.80. error = (4.8 – 4.74)/4.74 = 1.25%
  • 6. Graph showing the regression line and the data points Regression line Data point
  • 7. Filling factor and thickness reduction
  • 8. Rolled width vs thickness reduction Plotted with Origin
  • 9. Quadratic model : y = a + bx + cx 2 ( http://www.physics.csbsju.edu/cgi-bin/stats/WAPP ) Sr = 40.03 + 0.01862r + 0.0009461r 2 Test with r = 35  Sr = 40.03 + 0.01862x35 + 0.0009461x35 2 = 41.84 Measured S r (35%) = 4.1.52 mm  error (relative) = (41.84 – 41.52)/41.52 = 0.77%
  • 10. Graph showing the regression curve and the data points Regression curve Data point
  • 11.  
  • 12. Friction factor ( m ) variation
  • 13. Friction factor variation data from DEFORM 4.22/4.76 4.47/40.97 4.57/40.68 0.60 4.27/41.73 4.44/41.02 4.50/40.65 0.40 4.27/41.70 4.48/41.05 4.54/40.76 0.35 4.28/41.75 4.51/41.04 4.53/40.79 0.30 4.25/41.90 4.48/41.17 4.53/40.82 0.25 4.18/42.28 4.47/41.24 4.57/40.89 0.20 4.22/42.36 4.45/41.27 4.59/40.96 0.15 40% 30% 20%
  • 14. Not significant effect on central height
  • 15.  Try parabolic model for (1) (1) On width… Half – quadratic curve
  • 16. Sr = 43.61 – 10.48m + 14.36m 2
    • Test with m = 0.20
    • Sr = 43.61 – 10.48x0.2 + 14.36x0.04)
    • = 42.09
    • Error = (42.28 – 42.09)/42.09
    • = 0.45%
  • 17. Quadratic graph
  • 18.
    • Central height & filling vs thickness reduction relationship can be treated with linear function
    • Spreading vs thickness reduction can be well treated with quadratic relationship
    • Friction does not affect central height
    • Spread vs friction can be described by a quadratic function
    • Upcoming: thickness, width, vacancy, inclined angle ,…
    Conclusions
  • 19. Appendix
  • 20. Appendix