Precision Machining Technology
3rd Edition
ISBN: 9781337795302
Author: Peter, Hoffman.
Publisher: Cengage Learning,
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Chapter 4.2, Problem 9RQ
If 50 parts measuring 1" × I" × 3" each needed a hole drilled in a side, which workholding device would be best?
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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 4 Solutions
Precision Machining Technology
Ch. 4.1 - Upright drill presses are available in _______ and...Ch. 4.1 - List two general types of upright drill press...Ch. 4.1 - Explain how the size of an upright drill press is...Ch. 4.1 - Briefly describe the term sensitive drill press.Ch. 4.1 - Briefly describe a gang drill press and its...Ch. 4.1 - When would a radial-arm drill press most likely be...Ch. 4.1 - Briefly describe a micro drill press and its...Ch. 4.2 - What are the two main materials used to make...Ch. 4.2 - What two types of shanks are commonly found on...Ch. 4.2 - Name three functions of the flutes on a twist...
Ch. 4.2 - Name two types of flute styles for machine...Ch. 4.2 - Prob. 5RQCh. 4.2 - What is the major difference between counterboring...Ch. 4.2 - What must be used to secure a workpiece to an...Ch. 4.2 - What devices are used to elevate a workpiece to...Ch. 4.2 - If 50 parts measuring 1" I" 3" each needed a...Ch. 4.2 - Which would be the best workholding device for...Ch. 4.2 - Which would be the best workholding device for...Ch. 4.2 - Which would be the best workholding device for...Ch. 4.3 - List five drill press safety guidelines.Ch. 4.3 - Briefly define the term cutting speed.Ch. 4.3 - What unit of measure is used to define cutting...Ch. 4.3 - What is feed, and how is feed stated for drill...Ch. 4.3 - Briefly describe two methods for locating hole...Ch. 4.3 - What is spotting and why is it performed?Ch. 4.3 - What is pecking, or peck drilling?Ch. 4.3 - Briefly contrast the speed and feed differences...Ch. 4.3 - What drill press component can be used to control...Ch. 4.3 - Calculate feed depth for a 90-degree countersink...Ch. 4.3 - Calculate feed depth for an 82-degree countersink...Ch. 4.3 - What benefit does tapping on the drill press offer...Ch. 4.3 - How many turns must a 1/4-20 tap be turned into a...Ch. 4.3 - Prob. 14RQ
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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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