Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Textbook Question
Chapter 24, Problem 1RQ
Explain why milling is such a versatile machining operation.
Expert Solution & Answer
To determine
Explain why milling is such a versatile machining operation.
Explanation of Solution
Milling comprises of many nifty machining processes, happening with many arrangements and alignments. It uses a milling cutter, described as a multi-tooth tool that creates a number of chips in a single revolution. Different operations of milling can be chosen to create a multitude of products, as per different requirements.
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 24 Solutions
Manufacturing Engineering & Technology
Ch. 24 - Explain why milling is such a versatile machining...Ch. 24 - Describe a milling machine. How is it different...Ch. 24 - Describe the different types of cutters used in...Ch. 24 - Define the following: face milling, peripheral...Ch. 24 - Can threads be machined on a mill? Explain.Ch. 24 - What is the difference between feed and feed per...Ch. 24 - Explain the relative characteristics of climb...Ch. 24 - Describe the geometric features of a broach and...Ch. 24 - What is a pull broach? A push broach?Ch. 24 - Why is sawing a commonly used process? Why do some...
Ch. 24 - What advantages do bed-type milling machines have...Ch. 24 - Explain why the axis of a hob is tilted with...Ch. 24 - What is a shell mill? Why is it used?Ch. 24 - Why is it difficult to saw thin sheet metals?Ch. 24 - Of the processes depicted in Fig. 24.2, which is...Ch. 24 - Describe the tool motion during gear shaping.Ch. 24 - When is filing necessary?Ch. 24 - Would you consider the machining processes...Ch. 24 - Why is end milling such an important versatile...Ch. 24 - List and explain factors that contribute to poor...Ch. 24 - Explain why broaching crankshaft bearings is an...Ch. 24 - Several guidelines are presented in this chapter...Ch. 24 - What are the advantages of helical teeth over...Ch. 24 - Explain why hacksaws are not as productive as band...Ch. 24 - What similarities and differences are there in...Ch. 24 - Why do machined gears have to be subjected to...Ch. 24 - How would you reduce the surface roughness shown...Ch. 24 - Why are machines such as the one shown in Fig....Ch. 24 - Comment on your observations concerning the...Ch. 24 - Explain how contour cutting could be started in a...Ch. 24 - Prob. 32QLPCh. 24 - Describe the parts and conditions under which...Ch. 24 - Explain the reason that it is difficult to use...Ch. 24 - Would you recommend broaching a keyway on a gear...Ch. 24 - Prob. 37QTPCh. 24 - A slab-milling operation is being performed at a...Ch. 24 - Show that the distance lc in slab milling is...Ch. 24 - Prob. 40QTPCh. 24 - Calculate the chip depth of cut, tc, and the...Ch. 24 - Estimate the time required to face mill a...Ch. 24 - A 12-in.-long, 1-in.-thick plate is being cut on a...Ch. 24 - A single-thread hob is used to cut 40 teeth on a...Ch. 24 - Assume that m the face-milling operation shown in...Ch. 24 - A slab-milling operation will take place on a part...Ch. 24 - Prob. 47QTPCh. 24 - In describing the broaching operations and the...Ch. 24 - The parts shown in Fig. 24.1 are to be machined...Ch. 24 - Would you prefer to machine the part in Fig. 24....Ch. 24 - Prob. 51SDPCh. 24 - Suggest methods whereby milling cutters of various...Ch. 24 - Prepare a comprehensive table of the process...Ch. 24 - Prob. 55SDPCh. 24 - Make a list of all the processes that can be used...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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