Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Textbook Question
Chapter 22, Problem 1RQ
What are the major properties required of cutting-tool materials? Why?
Expert Solution & Answer
To determine
What are the major properties required of cutting-tool materials? Why?
Explanation of Solution
A cutting-tool material should have the below attributes:-
Hot hardness
Wear resistance coupled with hardness and strength of the tool stay intact at the temperatures experienced in machining operations. This property is responsible for making sure that the tool would not go through any plastic deformation. That is how it retains its sharpness and forms both.
Toughness and strength of impact
In interfered cutting tasks or forces like milling, and then turning a splined shaft on a lathe, the forces of impact on the tools is experienced time and again. This is because of vibration and chatter amid machining. But this neither chip nor break the tool.
Thermal shock resistance
To bear the fast temperature cycling, as experienced in interfered cutting.
Wear resistance
With the goal that a long-enough tool life is acquired before substituting becomes inevitable.
Chemical stability and inactiveness
Concerning the workpiece material, to evade or limit any unfavorable reactions, adhesion, and tool–chip diffusion which may fasten the wear of the tool.
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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 22 Solutions
Manufacturing Engineering & Technology
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