Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Textbook Question
Chapter 12, Problem 1RQ
Why are steels more difficult to cast than cast irons?
Expert Solution & Answer
To determine
Why are steels more difficult to cast than cast irons?
Explanation of Solution
The steels melt at high temperatures (1650C). It also helps in the reactions of steels with oxygen in high intensity during melting and pouring of metal.
At times, the fluidity of molten steel is not good enough to be casted. Because there is increased amount of Silicon present in Cast Iron, its fluidity is more than that of Steel. But in some of the steels, increased amount of silicon is present.
The defect “MISRUN” comes into scene due to low fluidity. This is actually the drawback of a material to completely fill the Sand Casting Mold.
Hence, steel is difficult to cast than cast iron.
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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 12 Solutions
Manufacturing Engineering & Technology
Ch. 12 - Why are steels more difficult to cast than cast...Ch. 12 - What is the significance of hot spots in metal...Ch. 12 - What is shrinkage allowance? Machining allowance?Ch. 12 - Explain the reason for drafts in molds.Ch. 12 - Prob. 5RQCh. 12 - What are light castings and where are they used...Ch. 12 - Name the types of cast irons generally available,...Ch. 12 - Comment on your observations regarding Fig. 12.5.Ch. 12 - Describe the difference between a runner and a...Ch. 12 - What is the difference between machining allowance...
Ch. 12 - What is dross? Can it be eliminated?Ch. 12 - Describe your observation concerning the design...Ch. 12 - If you need only a few castings of the same...Ch. 12 - Do you generally agree with the cost ratings in...Ch. 12 - Describe the nature of the design differences...Ch. 12 - Note in Fig. 12.5 that the ductility of some cast...Ch. 12 - Do you think that there will be fewer defects in a...Ch. 12 - Explain the difference in the importance of drafts...Ch. 12 - What type of cast iron would be suitable for...Ch. 12 - Explain the advantages and limitations of sharp...Ch. 12 - Explain why the elastic modulus, E, of gray cast...Ch. 12 - If you were to incorporate lettering or numbers on...Ch. 12 - The general design recommendations for a well in...Ch. 12 - The heavy regions of parts typically are placed in...Ch. 12 - What are the benefits and drawbacks to having a...Ch. 12 - When designing patterns for casting, patternmakers...Ch. 12 - Using the information given in Table 12.2, develop...Ch. 12 - The part in Figure P12.28 is to be cast of 10% Sn...Ch. 12 - Describe the general design considerations...Ch. 12 - Add more examples of applications to those shown...Ch. 12 - Explain how ribs and serrations are helpful in...Ch. 12 - List casting processes that are suitable for...Ch. 12 - Small amounts of slag and dross often persist...Ch. 12 - If you need only a few units of a particular...Ch. 12 - For the cast metal wheel illustrated in Fig....Ch. 12 - Assume that the introduction to this chapter is...Ch. 12 - In Fig. P12.37, the original casting design shown...Ch. 12 - An incorrect and a correct design for casting are...Ch. 12 - Using the method of inscribed circles, shown in...Ch. 12 - A growing trend is the production of patterns and...Ch. 12 - Repeat Problem 12.40 for the case where (a) a...
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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
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