1GEORGIA INSTITUTE OF TECHNOLOGY George W. Woodruff School of Mechanical Engineering ME 4210 MANUFACTURING PROCESSES AND ENGINEERING Spring 2008 Quiz #1 February 8 Be sure to list all assumptions. Put all your work and answers in the "blue book". Write legibly. There are two (2) questions. Closed books and notes. Only a calculator and writing implements are allowed. This exam is 50 minutes long. Problem #1 (50 points) You are casting an aluminum part in a sand mold. The part is a rectangular solid with dimensions of 10 cm width, 2 cm depth, and a height of 40 cm. The part is bottom gated with a cylindrical gate with diameter of 1 cm. The mold temperature is initially 25 C. At what temperature should you pour the metal?2Material properties: Data for solid materials (room temperature) Material Specific heat (C) (kJ/kg-oC) Density (ρ) (kg/m3) Thermal conductivity (k) (W/m-oC) Thermal diffusivity (α) (m2/s) Sand 1.16 1500 0.60 3.45 x 10-7 Aluminum 0.90 2700 202 8.31 x 10-5 Nickel 0.44 8910 92 2.35 x 10-5 Magnesium 1.07 1700 156 8.58 x 10-5 Copper 0.39 8970 385 1.1 x 10-5 Gray cast iron 0.441 7125 42.7 1.36 x 10-5 Data for liquid materials Material Melting point (oC) Latent heat of solidification (fusion) (Hf) (kJ/kg) Specific heat (C) (kJ/kg-oC) Viscosity (μ) (mPa-s) Aluminum 660 396 1.05 1.3 Nickel 1453 297 0.73 4.01 Magnesium 650 384 1.38 1.04 Copper 1083 220 0.52 2.1 Gray cast iron 1251 211 0.34 5.25 Solidification time (t) for an insulating mold (α mold << α casting; k mold << k casting) 22,int_14⎟⎟⎠⎞⎜⎜⎝⎛⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛−Δ=castingcastingmoldmoldmoldinitialmoldpomeltingcastingcastingAVCkTTHtρρπ Solidification time (t) for a conducting mold (Biot # =hl/k casting < 0.17) ()⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−Δ=castingcastingmoldpomeltingcastingcastingAVTThHtint_ρ ΔH = latent heat for the process = Hf + ΣCiΔT Hf = latent heat of solidification (fusion) V = volume A = area h = heat transfer coefficient C = specific heat ρ = density3Cooling time (t) for a solid object for a small Biot number (Biot # =hl/k casting < 0.17) Chvorinov’s rule for solidification time for an insulating mold t = K (V/A)2 t = cooling time K = a constant V = volume A = area Chvorinov’s rule for solidification time for a conducting mold t = K (V/A) Bernoulli's equation Reynold's number (good to keep below 20,000) Conservation of mass Q = A0v0 = A1v1 Filling time for a bottom-gated mold ()moldtotaltotalgatemoldfhhhgAAt −−=22 For no aspiration totalbapouringsprueofbottomsprueoftopsprueoftopsprueofbottomhhvvAAsin== ⎟⎟⎠⎞⎜⎜⎝⎛−−=finalcastingmoldinitialcastingmoldcastingcastingcastingcastingTTTThCAVt,,lnρμρVd=RefghvPghvPooo+++=++1211222ρρρρ4 Mold filling time estimate gategatevAvolumeMoldt = Thermal Diffusivity ckρα=5Problem #2 (50 points) You are forging a rectangular piece of metal. Its initial dimensions are 100 mm x 100 mm x 1500 mm (width x height x length into “board”). You are reducing its height by total of 50% at a rate of 0.5 m/min. The metal being forged has K= 315 MPa, n = 0.54; C = 450 MPa and m = 0.1. The coefficient of friction is 0.213. The forge has a power of 100 MW. Would you use hot or cold forging? Be quantitative in your discussion. NOTE: All pressure equations are on a “per unit depth” basis. Sliding pressure at a point Average sliding pressure (x < xk): Sliding/sticking transition: Sticking pressure at a point (xk < x < w/2): Average sticking pressure (xk < x < w/2): ⎟⎠⎞⎜⎝⎛=hxPflowxμτ2exp2μμ21ln21=hxkhxPflowx+⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−=μμτ21ln1212⎥⎦⎤⎢⎣⎡−⎟⎠⎞⎜⎝⎛⋅= 12exp22 hxxhpkkflowaveμμτkkkflowavexwxwhxwp−⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛−+⎟⎠⎞⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−=2421221ln121222μμτ6 Strain hardening material: nflowKετ15.12 = ⎟⎟⎠⎞⎜⎜⎝⎛=fihhlnε Strain rate material mflowCετ&15.12 = taenousinsplatenhvtan=ε& Power = force x
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