Degarmo's Materials And Processes In Manufacturing
13th Edition
ISBN: 9781119492825
Author: Black, J. Temple, Kohser, Ronald A., Author.
Publisher: Wiley,
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Chapter 20, Problem 40RQ
What are some of the ways in which metal inserts are held in place in a plastic part?
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Spur gears
Note : Exam is open notes &tables / Answer all questions.
Q.1. The press shown for Figure.1 has a rated load
of 22 kN. The twin screws have double start Acme
threads, a diameter of 50 mm, and a pitch of 6 mm.
Coefficients of friction are 0.05 for the threads and
0.08 for the collar bearings. Collar diameters are 90
mm. The gears have an efficiency of 95 percent and a
speed ratio of 60:1. A slip clutch, on the motor shaft,
prevents overloading. The full-load motor speed is
1720 rev/min.
(a) When the motor is turned on, how fast will the
press head move? (Vm= , Vser. =
)
(5M)
(b) What should be the horsepower rating of the
motor? (TR=, Tc= Pser. =
"
Bronze
bushings
Foot
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watt, Pm= watt, Pm= h.p.) (20M)
2['s
Fig.1
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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 20 Solutions
Degarmo's Materials And Processes In Manufacturing
Ch. 20 - Why are the fabrication processes applied to...Ch. 20 - How does the fabrication of a shaped product from...Ch. 20 - What are some of the methods used to shape...Ch. 20 - What are some of the ways that plastic sheet,...Ch. 20 - Prob. 5RQCh. 20 - What types of polymers are most commonly blow...Ch. 20 - What are some common blow molded products, in...Ch. 20 - Why do blow molding molds typically contain a...Ch. 20 - Prob. 9RQCh. 20 - Prob. 10RQ
Ch. 20 - Prob. 11RQCh. 20 - Prob. 12RQCh. 20 - Prob. 13RQCh. 20 - Prob. 14RQCh. 20 - Prob. 15RQCh. 20 - What are some of the benefits of a hot runner...Ch. 20 - Why is the cycle time for the injection molding of...Ch. 20 - Prob. 18RQCh. 20 - Prob. 19RQCh. 20 - What are some of the ways by which a polymer...Ch. 20 - Prob. 21RQCh. 20 - How can the extrusion process be used to produce...Ch. 20 - Prob. 23RQCh. 20 - Prob. 24RQCh. 20 - Prob. 25RQCh. 20 - What is the difference between open-cell and...Ch. 20 - Prob. 27RQCh. 20 - What types of products are produced by...Ch. 20 - Prob. 29RQCh. 20 - What are some of the general properties of...Ch. 20 - What are some of the attractive features of laser...Ch. 20 - What property of plastics is responsible for...Ch. 20 - Prob. 33RQCh. 20 - Prob. 34RQCh. 20 - Prob. 35RQCh. 20 - Prob. 36RQCh. 20 - Prob. 37RQCh. 20 - Prob. 38RQCh. 20 - Why might threaded inserts be preferred over other...Ch. 20 - What are some of the ways in which metal inserts...Ch. 20 - Prob. 41RQCh. 20 - Why does locating a parting line on a sharp corner...Ch. 20 - Prob. 43RQCh. 20 - Prob. 44RQCh. 20 - Prob. 45RQCh. 20 - What property changes occur during vulcanization?Ch. 20 - Prob. 47RQCh. 20 - Prob. 48RQCh. 20 - How are glass fibers produced?Ch. 20 - Prob. 50RQCh. 20 - Prob. 51RQCh. 20 - What are glass-ceramics? How are they produced?Ch. 20 - Prob. 53RQCh. 20 - Describe the differences between the injection...Ch. 20 - Prob. 55RQCh. 20 - What is the difference between slip casting and...Ch. 20 - Prob. 57RQCh. 20 - Prob. 58RQCh. 20 - How does cementation differ from sintering?Ch. 20 - What are the benefits and limitations of machining...Ch. 20 - Prob. 61RQCh. 20 - Why are joining operations usually avoided when...Ch. 20 - Prob. 63RQCh. 20 - Discuss some of the design guidelines that relate...Ch. 20 - Prob. 65RQCh. 20 - Why are the processes used to fabricate...Ch. 20 - How are metals and ceramics combined in the...Ch. 20 - What are some of the processes that can be used to...Ch. 20 - What conditions might be attractive for...Ch. 20 - Prob. 70RQCh. 20 - Prob. 71RQCh. 20 - Prob. 72RQCh. 20 - Prob. 73RQCh. 20 - What are some of the ways that liquefied matrix...Ch. 20 - Prob. 75RQCh. 20 - Prob. 76RQCh. 20 - Prob. 77RQCh. 20 - In what way is pultrusion similar to wire drawing?Ch. 20 - Prob. 79RQCh. 20 - What are some typical products that are made by...Ch. 20 - Prob. 81RQCh. 20 - Prob. 82RQCh. 20 - Prob. 83RQCh. 20 - Prob. 84RQCh. 20 - Prob. 85RQCh. 20 - Prob. 86RQCh. 20 - What is the difference between reaction injection...Ch. 20 - Prob. 88RQCh. 20 - Prob. 89RQCh. 20 - What is a common property objective in...Ch. 20 - Prob. 91RQCh. 20 - Prob. 92RQCh. 20 - Prob. 93RQCh. 20 - What is the major concern when considering the...Ch. 20 - Prob. 95RQCh. 20 - Prob. 1PCh. 20 - Figure 20.A depicts the handles of two large...Ch. 20 - Tires are the dominant product of the rubber...Ch. 20 - Prob. 4PCh. 20 - Prob. 6PCh. 20 - Prob. 8PCh. 20 - Prob. 1.1CSCh. 20 - For plastic (high-density polyethylene)...Ch. 20 - What might be the pros and cons of weldable...Ch. 20 - Prob. 1.5CSCh. 20 - Prob. 1.6CSCh. 20 - Prob. 1.7CSCh. 20 - Crashworthiness is an important safety...Ch. 20 - Prob. 1.9CSCh. 20 - Prob. 1.10CSCh. 20 - Prob. 1.11CSCh. 20 - Prob. 2.1CSCh. 20 - Prob. 2.2CSCh. 20 - Prob. 2.3CSCh. 20 - Prob. 2.4CSCh. 20 - Prob. 2.5CS
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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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