Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Chapter 13, Problem 2RQ
Define roll gap, neutral point, and draft.
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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.
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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.
Chapter 13 Solutions
Manufacturing Engineering & Technology
Ch. 13 - What is the difference between a plate and a...Ch. 13 - Define roll gap, neutral point, and draft.Ch. 13 - What factors contribute to spreading in flat...Ch. 13 - What is forward slip? Why is it important?Ch. 13 - Describe the types of deflections that rolls...Ch. 13 - Describe the difference between a bloom, a slab,...Ch. 13 - Why may roller leveling be a necessary operation?Ch. 13 - List the defects commonly observed in flat...Ch. 13 - What are the advantages of tandem rolling? Pack...Ch. 13 - How are seamless tubes produced?
Ch. 13 - Why is the surface finish of a rolled product...Ch. 13 - What is a Sendzimir mill? What are its important...Ch. 13 - What is the Mannesmann process? How is it...Ch. 13 - Describe ring rolling. Is there a neutral plane in...Ch. 13 - How is back tension generated?Ch. 13 - Explain why the rolling process was invented and...Ch. 13 - Flat rolling reduces the thickness of plates and...Ch. 13 - Explain how the residual stress patterns shown in...Ch. 13 - Explain whether it would be practical to apply the...Ch. 13 - Describe the factors that influence the magnitude...Ch. 13 - Explain how you would go about applying front and...Ch. 13 - What typically is done to make sure that the...Ch. 13 - Make a list of parts that can be made by (a) shape...Ch. 13 - Describe the methods by which roll flattening can...Ch. 13 - It was stated that spreading in flat rolling...Ch. 13 - Flat rolling can be carried out by front tension...Ch. 13 - Explain the consequence of applying too high a...Ch. 13 - Note in Fig. 13.3f that the driven rolls (powered...Ch. 13 - Describe the importance of controlling roll...Ch. 13 - In Fig. 13.9a, if you remove the top compressive...Ch. 13 - Name several products that can be made by each of...Ch. 13 - List the possible consequences of rolling at (a)...Ch. 13 - It is known that in thread rolling, as illustrated...Ch. 13 - If a rolling mill encounters chatter, what process...Ch. 13 - Can the forward slip ever become negative? Why or...Ch. 13 - In Example 13.1, calculate the roll force and the...Ch. 13 - Calculate the individual drafts in each of the...Ch. 13 - Estimate the roll force, F, and the torque for an...Ch. 13 - A rolling operation takes place under the...Ch. 13 - Estimate the roll force and power for annealed...Ch. 13 - A flat-rolling operation is being carried out...Ch. 13 - A simple sketch of a four-high mill stand is shown...Ch. 13 - Obtain a piece of soft, round rubber eraser, such...Ch. 13 - If you repeat the experiment in Problem 13.45 with...Ch. 13 - Design a set of rolls to produce cross-sections...Ch. 13 - Design an experimental procedure for determining...Ch. 13 - Derive an expression for the thickest workpiece...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 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.arrow_forwardProblem 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_forward
- Problem 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_forwardI 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_forward
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