PRECISION MACHINING TECHNOLOGY PACKAGE
3rd Edition
ISBN: 9780357262788
Author: Hoffman
Publisher: CENGAGE L
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Textbook Question
Chapter 6.3, Problem 7RQ
What are two benefits of boring over other holemaking operations?
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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 6 Solutions
PRECISION MACHINING TECHNOLOGY PACKAGE
Ch. 6.1 - What part of the vertical milling machine allows...Ch. 6.1 - Briefly describe the direction of movement...Ch. 6.1 - When a table handle is turned clockwise the table...Ch. 6.1 - What distance does the saddle or table usually...Ch. 6.1 - Prob. 5RQCh. 6.1 - Briefly describe the function of the turret and...Ch. 6.1 - What is the name of the taper found in most modem...Ch. 6.1 - What part of the vertical mill can be raised and...Ch. 6.1 - How can power quill feed be automatically stopped...Ch. 6.1 - What is a benefit of using a DRO instead of...
Ch. 6.2 - Many of the cutters used in machining are made of...Ch. 6.2 - What is the major advantage of using...Ch. 6.2 - Prob. 3RQCh. 6.2 - What type of cutting tool would most likely be...Ch. 6.2 - Which type of cutter would most likely be used to...Ch. 6.2 - What workpiece factors might cause a four-flute...Ch. 6.2 - List three types of milling cutters that are used...Ch. 6.2 - Most manual vertical milling machine spindles are...Ch. 6.2 - A __________ is used to retain the toolholder in...Ch. 6.2 - What type of toolholder might he selected for...Ch. 6.2 - Sketch a corner-rounding endmill.Ch. 6.2 - What toolholding device uses two drive keys and a...Ch. 6.2 - Prob. 13RQCh. 6.2 - List the four basic pieces of a step clamp set: a....Ch. 6.2 - Prob. 15RQCh. 6.2 - Irregularly shaped work may be held in a custom...Ch. 6.3 - List five safety guidelines to observe when...Ch. 6.3 - Briefly describe the process of aligning a milling...Ch. 6.3 - What is chip load?Ch. 6.3 - Define IPM.Ch. 6.3 - Calculate spindle speed and feed for the two...Ch. 6.3 - Briefly describe the process of locating the...Ch. 6.3 - What are two benefits of boring over other...Ch. 6.3 - What are face milling and peripheral milling?Ch. 6.3 - When squaring a block on the vertical mill, what...Ch. 6.3 - What are the three basic methods used to mill...Ch. 6.3 - What must first be done before milling with either...Ch. 6.3 - Prob. 12RQCh. 6.3 - What diameter cutter should be used to create...Ch. 6.3 - When roughing a pocket, should you machine in a...Ch. 6.4 - What is a rotary axis?Ch. 6.4 - Define the term indexing.Ch. 6.4 - Describe the primary differences between the...Ch. 6.4 - Name three types of workpiece features that are...Ch. 6.4 - Briefly describe the two alignment steps that need...Ch. 6.4 - If the outside of a 6"-diameter disk is to be...Ch. 6.4 - What is the gear ratio found in the gear train of...Ch. 6.4 - When using the indexing head, a __________ can be...Ch. 6.4 - A workpiece requires 9 divisions. Calculate the...Ch. 6.4 - In the formula 40D=T,what do T and D represent?
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- 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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