Question

Part 1–Orthogonal Milling (50 points): Calculate the cutting force for the following parameters (64 calculations- spreadsheet or Matlab recommended): • Rake angles of 0, 5, 10, and 15 degrees • Coefficients of friction (u) of 0.1, 0.2, 0.3. and 0.4 Aluminum (6061-T6), Inconel (600), 1018 Steel (Annealed), and Titanium (Titanium Ti-6A1-4V (Grade 5), Annealed) Assumptions: • Thrust force = 1/4 cutting force Uncut chip thickness of .05" • Chip width of .15” Comment on the results—e.g. which combination results in the lowest/highest cutting force?

Answer 1

Model calculation for rake angle 5, coefficient of friction 0.2 of Inconel (600) material Chip thickness ratio is given by, Uncut chip thickness_to cut chip thickness 1. 0.05 = 0.333 0.15 1 = Rake angle(a), Friction angle (B) Shear angle is given by, r cos a o= tan 1-r sin a 0.333 cos 5 ø= tan- 1-0.33 sin 5 0=18.88 Friction angle is given by, B=tan(u) B = tam-(0-2) B=11.309

Shear strength (yield strength) (c) of Inconel (600) material is 41 ksi. Assumption: Depth of cut is 1 in. Shear force is given by, F = 41x tw F, = 0, sin 0.05x1 sin 18.88 0.05x1 sin 18.88 F = 6.335 kips F = 41x Cutting force, FI F 4 F = 4F1 sin(B-a) F = 4F cos($+B-a) sin (11.31-5) F = 4x6.335x COS (18.88+11:31-5) F = 3.077kips

chip ratio 0.3333333 Shear strength of Inconel 600 (in ksi) 41 S.No Coefficient shear force cutting Rake angle shear angle of friction Friction angle (kip) force (kip) 1 0 18.434949 0.1 5.710593137 6.4826692 2.82758621 2 0 18.434949 0.2 11.30993247 6.4826692 5.85714286 3 0 18.434949 0.3 16.69924423 6.4826692 9.11111111 4 0 18.434949 0.4 21.80140949 6.4826692 12.6153846 5 5 18.880723 0.1 5.710593137 6.3349994 0.33357461 6 5 18.880723 0.2 11.30993247 6.3349994 3.07773701 7 5 18.880723 0.3 16.69924423 6.3349994 5.96838557 8 5 18.880723 0.4 21.80140949 6.3349994 9.01757132 9 10 19.210267 0.1 5.710593137 6.2303238 -1.9290141 10 10 19.210267 0.2 11.30993247 6.2303238 0.60831525 11 10 19.210267 0.3 16.69924423 6.2303238 3.23213681 12 10 19.210267 0.4 21.80140949 6.2303238 5.94694981 13 15 19.411224 0.1 5.710593137 6.1682722 -4.0457301 14 15 19.411224 0.2 11.30993247 6.1682722 -1.6496537 15 15 19.411224 0.3 16.69924423 6.1682722 0.78426646 16 15 19.411224 0.4 21.80140949 6.1682722 3.25693421 Maximum 12.6153846 Minimum -4.0457301

chip ratio 0.3333333 Shear strength of Aliminium (in ksi) 30 S.No ܢܙ Coefficient shear force cutting Rake angle shear angle of friction Friction angle (kip) force (kip) 0 18.434949 0.1 5.710593137 4.7434165 2.06896552 2 0 18.434949 0.2 11.30993247 4.7434165 4.28571429 3 0 18.434949 0.3 16.69924423 4.7434165 6.66666667 4 0 18.434949 0.4 21.80140949 4.7434165 9.23076923 5 5 18.880723 0.1 5.710593137 4.6353654 0.24407898 6 5 18.880723 0.2 11.30993247 4.6353654 2.25200269 7 5 18.880723 0.3 16.69924423 4.6353654 4.36711139 8 5 18.880723 0.4 21.80140949 4.6353654 6.59822292 9 10 19.210267 0.1 5.710593137 4.5587735 -1.4114737 10 10 19.210267 0.2 11.30993247 4.5587735 0.44510872 11 10 19.210267 0.3 16.69924423 4.5587735 2.36497816 12 10 19.210267 0.4 21.80140949 4.5587735 4.35142669 13 15 19.411224 0.1 5.710593137 4.5133699 -2.9602903 14 15 19.411224 0.2 11.30993247 4.5133699 -1.2070637 15 15 19.411224 0.3 16.69924423 4.5133699 0.57385351 16 15 19.411224 0.4 21.80140949 4.5133699 2.38312259 Maximum 9.23076923 Minimum -2.9602903

chip ratio 0.3333333 Shear strength of steel 1018 (in ksi) 53.7 S.No ܢܙ Coefficient shear force cutting Rake angle shear angle of friction Friction angle (kip) force (kip) 0 18.434949 0.1 5.710593137 8.4907155 3.70344828 2 0 18.434949 0.2 11.30993247 8.4907155 7.67142857 3 0 18.434949 0.3 16.69924423 8.4907155 11.9333333 4 0 18.434949 0.4 21.80140949 8.4907155 16.5230769 5 5 18.880723 0.1 5.710593137 8.2973041 0.43690138 6 5 18.880723 0.2 11.30993247 8.2973041 4.03108481 7 5 18.880723 0.3 16.69924423 8.2973041 7.8171294 8 5 18.880723 0.4 21.80140949 8.2973041 11.810819 9 10 19.210267 0.1 5.710593137 8.1602046 -2.526538 10 10 19.210267 0.2 11.30993247 8.1602046 0.79674461 11 10 19.210267 0.3 16.69924423 8.1602046 4.2333109 12 10 19.210267 0.4 21.80140949 8.1602046 7.78905377 13 15 19.411224 0.1 5.710593137 8.0789322 -5.2989196 14 15 19.411224 0.2 11.30993247 8.0789322 -2.160644 15 15 19.411224 0.3 16.69924423 8.0789322 1.02719778 16 15 19.411224 0.4 21.80140949 8.0789322 4.26578944 Maximum 16.5230769 Minimum -5.2989196

A B - C E F H 5 6 7 chip ratio 0.3333333 Shear strength of Titanium (in ksi) 79.8 8 S.No 9 10 11 12 13 Uuuu O O O O 14 Coefficient shear force cutting Rake angle shear angle of friction Friction angle (kip) force (kip) 1 18.434949 0.1 5.710593137 12.617488 5.50344828 2 0 18.434949 0.2 11.30993247 12.617488 11.4 3 18.434949 0.3 16.69924423 12.617488 17.7333333 4 18.434949 0.4 21.80140949 12.617488 24.5538462 5 18.880723 0.1 5.710593137 12.330072 0.6492501 6 18.880723 0.2 11.30993247 12.330072 5.99032715 7 5 18.880723 0.3 16.69924423 12.330072 11.6165163 8 5 18.880723 0.4 21.80140949 12.330072 17.551273 9 10 19.210267 0.1 5.710593137 12.126338 -3.7545201 10 10 19.210267 0.2 11.30993247 12.126338 1.18398919 11 10 19.210267 0.3 16.69924423 12.126338 6.2908419 12 10 19.210267 0.4 21.80140949 12.126338 11.574795 13 15 19.411224 0.1 5.710593137 12.005564 -7.8743722 14 15 19.411224 0.2 11.30993247 12.005564 -3.2107895 15 15 19.411224 0.3 16.69924423 12.005564 1.52645033 16 15 19.411224 0.4 21.80140949 12.005564 6.33910609 Maximum 24.5538462 Minimum -7.8743722 15 16 17 18 19 20 21 22 23 24 25 26

Excel formulas:

Shear angle =DEGREES(ATAN(($D$6*COS(C9*PI()/180))/(1-($D$6*SIN(C9*PI()/180)))))

shear force =$I$6*((0.05*1)/(SIN(D9*PI()/180)))

cutting force  =4*G9*(SIN((F9-C9)*PI()/180))/(COS((D9+F9-C9)*PI()/180))

Comments:

Maximum value (titanium, 0 rake angle, 0.4 friction ): 15.34 kips

Minimum value (titanium, 15 rake angle, 0.1 friction): -7.8 kips

Please comment, if you need any help.