EBK MANUFACTURING ENGINEERING & TECHNOL
7th Edition
ISBN: 9780100793439
Author: KALPAKJIAN
Publisher: YUZU
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Chapter 26, Problem 12RQ
What is the purpose of the slurry in chemical–mechanical polishing?
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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
Motor
Bearings
watt, Pm= watt, Pm= h.p.) (20M)
2['s
Fig.1
Worm
Collar
bearing
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 26 Solutions
EBK MANUFACTURING ENGINEERING & TECHNOL
Ch. 26 - What is an abrasive? What are superabrasives?Ch. 26 - How is the size of an abrasive grain related to...Ch. 26 - Why are most abrasives made synthetically?Ch. 26 - Describe the structure of a grinding wheel and its...Ch. 26 - Explain the characteristics of each type of bond...Ch. 26 - What causes grinding sparks in grinding? Is it...Ch. 26 - Define metallurgical burn.Ch. 26 - Define (a) friability, (b) wear flat, (c) grinding...Ch. 26 - What is creep-feed grinding and what are its...Ch. 26 - How is centerless grinding different from...
Ch. 26 - What are the differences between coated and bonded...Ch. 26 - What is the purpose of the slurry in...Ch. 26 - Explain why grinding operations may be necessary...Ch. 26 - Why is there such a wide variety of types, shapes,...Ch. 26 - Prob. 15QLPCh. 26 - The grinding ratio, G, depends on the type of...Ch. 26 - What are the consequences of allowing the...Ch. 26 - Explain why speeds are much higher in grinding...Ch. 26 - Prob. 19QLPCh. 26 - Prob. 20QLPCh. 26 - Prob. 21QLPCh. 26 - Referring to the preceding chapters on processing...Ch. 26 - Explain the reasons that so many deburring...Ch. 26 - What precautions should you take when grinding...Ch. 26 - Prob. 25QLPCh. 26 - What factors could contribute to chatter in...Ch. 26 - Prob. 27QLPCh. 26 - Prob. 28QLPCh. 26 - Describe the effects of a wear flat on the overall...Ch. 26 - What difficulties, if any, could you encounter in...Ch. 26 - Prob. 31QLPCh. 26 - Prob. 32QLPCh. 26 - Prob. 33QLPCh. 26 - Jewelry applications require the grinding of...Ch. 26 - List and explain factors that contribute to poor...Ch. 26 - Calculate the chip dimensions in surface grinding...Ch. 26 - If the strength of the workpiece material is...Ch. 26 - Assume that a surface-grinding operation is being...Ch. 26 - Estimate the percent increase in the cost of the...Ch. 26 - Assume that the energy cost for grinding an...Ch. 26 - It is known that, in grinding, heat checking...Ch. 26 - Prob. 45QTPCh. 26 - With appropriate sketches, describe the principles...Ch. 26 - Prob. 47SDPCh. 26 - Vitrified grinding wheels (also called ceramic...Ch. 26 - Conduct a literature search, and explain how...Ch. 26 - Visit a large hardware store and inspect the...Ch. 26 - Obtain a small grinding wheel or a piece of a...Ch. 26 - In reviewing the abrasive machining processes in...Ch. 26 - Obtain pieces of sandpaper and emery cloth of...Ch. 26 - On the basis of the contents of this chapter,...
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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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