w11-hw2-dim-tol-stat-mat

# w11-hw2-dim-tol-stat-mat - ME250 Design and Manufacturing I...

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Unformatted text preview: ME250 Design and Manufacturing I Winter 2011 Lecture HW #2 Name: ___________________________ UMID: _________________ Lab Section #: _______ Note: You must indicate name, UMID, and Lab Section # otherwise the homework will not be returned. 1. Draw orthographic views of the following object and dimension them. [25 pts] Front view 2. Fill the table with MMC and LMC values corresponding to features A—F. [15 pts] 3. The flange joint assembly for a pressure vessel is shown in the figure below. A No. 370 O ring is to be installed in the gland in order to avoid the leakage. The gland dimensions are G = 7.24 ± 0.13 [mm], F = 4.32 ± 0.13 [mm], and Y = 218.48 ± 1.10 [mm]. The outside diameter of No. 370 O ring is 219.58 ± 0.34 [mm] and the cross‐ sectional diameter is 5.33 ± 0.13 [mm]. [30 pts] end plate Y O ring G G gland F (a) When the end plate is bolted in position, the O ring is compressed. Assuming absolute tolerance, what is the amount of the minimum compression (squeeze) [mm] of the O ring? (10 pts) (b) Assuming statistical tolerances, what is the probability that the O ring is circumferentially compressed when the O ring is placed in the gland prior to assembly of the end plate? Note that this is a desired situation since adequate compression can help sealing. (10 pts) (c) Assuming statistical tolerances, what is the probability that the O ring is circumferentially stretched when the O ring is placed in the gland prior to assembly of the end plate? Assume the cross‐sectional diameter of the O ring at one location is independent of the cross‐sectional diameter at another location. Assume the same for the width G of the gland. Note that this is an undesired situation since stretching an O ring can cause poor sealing. (10 pts) 4. Global bending of a vehicle chassis can be approximately modeled as bending of a simply supported plate under distributed load. In the figure below, b, h, and l are the width, the thickness, and the length between supports of a plate, respectively, and w is a load per unit length that is applied on the plate. w h l b The plate is made of a material with the density and Young’s modulus E. The maximum allowable displacement of the plate is 0 and we are interested in minimizing the mass of the plate, m, for given l and b which are specified by the overall vehicle size. The 2nd moment of area of the cross section of the plate is given by I bh3 /12 and the maximum displacement (occurs at a half of the length) is given by: 5wl 4 384 EI Answer the following. [30pts] (a) Express m with respect to the given quantities. [5pts] (b) For given b, l, w and 0, show that material index (to be maximized) for selecting the material minimizing m is E1/3/Note that h is a free variable that should be eliminated in your calculation. [5pts] (c) Using the line selection method with bubble chart in CES EduPack software, select three materials for the chassis that maximize the material index in (b) with 0.5×106 psi ≤ E ≤ 10×106 psi. Use the “Edu Level 2: Materials” data. Attach the printout of the bubble chart with the selection line. [10pts] (d) Consider now the material used for the semester project, PVC (E = 421000 psi and Sy = 7500 psi). What is the minimum value of h so that the displacement can be kept below 0? Use b = 2.0 in, l = 5.0 in, w = 0.30 lb/in, and 0 = 0.10 in. [5pts]. (e) The maximum stress (occurs on the top and bottom surfaces at a half of the length) is given by: wl 2 h 16 I Using the same values for b, l, w, and 0 as in (d) and the minimum thickness obtained in (d), calculate the factor of safety of the chassis. [5pts] ...
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## This note was uploaded on 09/12/2011 for the course MECHENG 250 taught by Professor Stevis during the Winter '09 term at University of Michigan.

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