quiz1_sol - Quiz 1 2.008 Design and Manufacturing II March...

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1 Quiz 1 2.008 Design and Manufacturing II March 17 th , 2004 Massachusetts Institute of Technology Department of Mechanical Engineering - There are four questions with 40, 30, 20, 10 points, respectively. - Closed book. - Subparts of each question have approximately equal points, if not marked. - You are given 75 minutes. - If you need more space, use the back of each page. (I doubt you need more space, since most answers would be short.) - Make sure you write down your name below. - Good luck!! Name: Solution
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Problem 1: (40 points) A 6 inch long, 1.5 inch diameter 304 stainless steel rod is going to be machined at the lathe into the geometry below. (Fig. 1-1) φ 3.0 φ1.4 6 φ 1.5 Fig. 1-1 The finished steel rod. a) Since you don’t know how to set the machining (turning) parameters, you decide to find them out by recalling the cutting physics lecture. First step is to name the diagram below assuming the job above is in the orthogonal cutting condition. Name the “?’s” in Fig. 1-2. (3 points) s s V F : shearing for Power c c V F : input Power c V F : friction via dissipated Power V t w V F u o s s s = : shearing for energy Specific V t w V F u o c f = : friction for energy Specific V t w V t w u u o o f s + = + : energy specific Total 3)? 1)? 2)? 5)? 6)? 4)? 1) Rake Angle 2) Secondary shear zone 3) Primary shear zone 4) relief or clearance angle 5) shear plane 6) shear angle Fig. 1-2 Orthogonal cutting b) In order to set the proper feed, speed, depth of cut, you need to find out the cutting force, power, etc. From the cutting force FBD in Fig 1-3-a), Merchant made a diagram to find out the shear plane and related parameters. (Fig. 1-3-b) 2
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Get the angles A, B, C, D, E in terms of α, β, φ. ( 2 points) D Α R F n F s F N F t F c E C Β A: _____ φ ______ B:______ β - α ____ C:______ β ______ D:______ α ______ E:_______ α _____ Fig 1-3 a) FBD of cutting b) Merchant’s diagram c) From the diagram in Fig. 1-3-b), Merchant derived the relationship among α, β, ϕ . Write down the relationship among α, β, ϕ ?(5 points)(You don’t need to derive it.) φ = 45 ° + α /2 - β /2 What was his assumption of locating the shear plane in deriving the above equation? (5 points) The shear plane adjusts its location to minimize the cutting force or maximize the shear stress. The tool given is HSS material with a rake angle of 10 o . The friction coefficient between the tool and the material given is 0.5. What is the shear angle, ϕ ? (5 points) The angle, β can be found from the relationship, µ = tan( β ) That means that β = arctan(0.5) = 26.6 ° From the problem statement, 3
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rake angle = 10 ° = α Therefore, from Merchant’s relationship, φ = 45 ° + 10 ° /2 – 26.6 ° /2 = 36.7 ° d) Now you set the turning parameters as below. Rotational speed, N=400 rpm, Tool travel speed along the work piece length, 12 inch/min, and the machining is going to be done by one pass. (15 points + 5 bonus points)
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.008 taught by Professor Jung-hoonchun during the Spring '04 term at MIT.

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quiz1_sol - Quiz 1 2.008 Design and Manufacturing II March...

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