11hw4-4feb-Soln - EML 4321 – HW #4 – Due 4 February...

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Unformatted text preview: EML 4321 – HW #4 – Due 4 February 2011 1. Molten metal is poured from above into a sprue with an initial vertical velocity of 5 ft/sec at the top of the sprue. If the top of the sprue is 1 inch in diameter, what should the diameter be 6 inches below the top? v = 2hg → 5 ft / s = 2h(32.2 ft / s 2 ) ; h = 0.388 ft hnew = 0.5 + 0.388 = 0.888 ft vnew = 2hg = 2 ⋅ 0.888 ⋅ 32.2 = 7.56 ft / s q = const. = Av = ⇒ x= 5 7.56 πd2 4 v→ ⎛ ⎝ 2 2 1 ft ⎞ 1 ft ⎞ ⎛ π ⋅ ⎜ x in ⋅ ⎟ ⎟ 12 in ⎠ 12 in ⎠ ⎝ ⋅ 5 ft / s = ⋅ 7.56 ft / s 4 4 π ⋅ ⎜1in ⋅ ∴ x = 0.81 in (ANS.) 2. A die casting mold is held shut by four hydraulic cylinders. If a one‐foot diameter sphere is being cast at 100 MPa, what force (tons) must each cylinder provide? F = pA = 100 ⋅106 Pa ⋅ π ⋅ (0.304 m)2 = 7.26 ⋅106 N = Ftotal = 4 Fcylinder 4 = 1.81 MN ≈ 202 tons (ANS.) → Fcylinder *1 foot = 0.304 m 3. Consider Figure 3.45. What force (tons) is necessary to press (no re‐pressing) the material before sintering to achieve 90% density after sintering of a 3” diameter cylindrical gear? Theorectical density in Fig .3.45 ≈ 7.9 g / cm3 90% of density ≈ 7.11 g / cm3 → Choose p = 600 MPa in Fig .3.45 2 ⎛ 0.0254 m ⎞ π ⋅ ⎜ 3 in ⋅ ⎟ 1in ⎠ = 2.74 ⋅106 N = 2.74 MN ≈ 308 tons (ANS.) F = pA = 600 ⋅106 Pa ⋅ ⎝ 4 *1 in = 0.0254 m 4. A strain hardening material obeys equation 5.7 with Y0=200 MPa and K=100 MPa. How much specific work (J/cm3) is required to achieve a true strain of 0.5? σ W = ∫ σ ⋅ dε = 100 200 0.5 ∫ (200 + 100ε )d ε 0 N⎞ 1⎛ N⎞ 2 ⎛ = ⎜ 200 ⎟ ⋅ ( 0.5 ) + ⋅ ⎜ 100 ⎟ ⋅ ( 0.5 ) mm 2 ⎠ 2⎝ mm 2 ⎠ ⎝ Nm J (ANS.) = 112.5 = 112.5 mm 2 m cm 3 ε 5. A rectangular‐cross‐section specimen is stretched in a tensile test. During the test it decreases in width from 20 mm to 15 mm while the thickness changes from 0.6 mm to 0.5 mm. a. What is the plastic strain ratio? Eqns in p.182 ⎛ w1 ⎞ ⎛ 15 mm ⎞ ⎟ = ln ⎜ ⎟ = −0.287 ⎝ 20 mm ⎠ ⎝ w0 ⎠ ε w = ln ⎜ ⎛h ⎞ ⎛ 0.5 ⎞ ε t = ln ⎜ 1 ⎟ = ln ⎜ ⎟ = −0.182 ⎝ 0.6 ⎠ ⎝ h0 ⎠ ε −0.287 = 1.577 ≈ 1.6 (ANS.) r= w = ε t −0.182 b. Is this material a good candidate for deep drawing? Yes (Ans.) 6. A forging press has a 2 tonne hammer that is dropped 1 meter. How much energy (J) can be imparted to the impacted forging? 1000 kg m ⋅ 9.81 2 ⋅1 m = 19620 J (ANS.) 1 tonne s 2 kg ⋅ m (1 J = 1 N ⋅ m = ) s2 E = mgh = 2 tonne ⋅ 7. A hydraulic press is actuated by four five‐inch‐diameter hydraulic cylinders. Oil at 3000 psi is supplied to the cylinders. a. What is the maximum force (tons) which the press can exert? π ⋅ 52 area F = pA = 3000 psi ⋅ ⋅ 4 cylinder = 235000 lbs ≈ 117.5 tons (ANS.) 4 cylinder b. What is the total flow (gpm) required to the cylinders if the press is to travel at 1 foot/second? q = vA = 1 foot 60 s 12 in π ⋅ 52 area (in 2 ) in3 ⋅ ⋅ 4 cylinder = 56548.66 4 cylinder s min foot min → 56548.66 in3 1 gallon ⋅ = 244.85 ≈ 245 gpm (ANS.) min 231in3 (231in3 = 1gallon) 8. A mechanical press has a 50 mm crank and a 600 mm link. If the crank is turning at 70 rpm, what is the maximum velocity (m/min) of the ram? (Note: whether to take the derivative of the velocity or just plot it to find the maximum is your choice.) Using corrected eqn 4.3, 2 ⎡ ⎤ ⎛r⎞ x = r (1 − cos φ ) − l ⎢1 − 1 − ⎜ ⎟ sin 2 φ ⎥ ; φ = 2π nt , r = 50 mm = 0.05 m, l = 600 mm = 0.6 m, n = 700 rpm ⎢ ⎥ ⎝l⎠ ⎣ ⎦ 2 2 ⎡ ⎤ ⎛r⎞ x = r (1 − cos 2π nt ) − l ⎢1 − 1 − ⎜ ⎟ sin 2 2π nt ⎥ ⎢ ⎥ ⎝l⎠ ⎣ ⎦ ⎛r⎞ l ⋅ ⎜ ⎟ ⋅ 2π n ⋅ sin 2π nt ⋅ cos 2π nt dx l ; vx = = 2π nr ⋅ sin 2π nt − ⎝ ⎠ 2 dt ⎛r⎞ 1 − ⎜ ⎟ sin 2 2π nt ⎝l⎠ The maximum velocity is 22.07 m/min when Ø≈95° ...
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This note was uploaded on 09/06/2011 for the course EML 4321 taught by Professor Staff during the Spring '08 term at University of Florida.

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